You would need to make an electric tank:
If this civilization has the ability to create mechas, and the rebels have limited access to the production facilities, then they have the ability to steal some very high tech equipment.
The drive train would be an 8 wheel tracked system driven by 250 hp permanent magnet electric motors on each wheel.It would have 2000hp in total. These would be easy to get access to because normal motors would burn out much easier and be replaced so the mechas would need to use some sort of permanent magnet motor which is much more rugged and reliable with a longer service life. The vehicle would have a lower heat signature, it would make much less noise and the drive train would be less mechanically complex owing to the fact that the motors not only take up less space, but have fewer moving parts and reduce the need for a large engine block. The fact that there are multiple drive systems means the vehicle can move even if one or two of the wheels are hacked off. The motors would also be much lighter than a massive engine. The axles of the motors would have miniature electrical generators attached so that the vehicle can partially recharge as it moves. Due to the advanced pneumatics and hydraulics used in a mecha the ability to make a pneumatic suspension system would be there, unless they opt for a cheaper one similar to the one in the merkava.
Power would be stored underneath the floor of the tank (between the floor and the underbelly armor) in layers upon layers of paper thin graphene super capacitors. These would propbably be used in the mechas due to the need for a compact power storage solution. They can recharged in as much time as it takes to fill a gas tank and can be discharged very quickly in case of a lower hull breach. This negates the need for a huge tank (no pun intended) containing volatile fuel. On the motors to cool them down is a system of solid state thermoelectric panels that absorb most heat emitted and turn it to electricity, same with other heat producing components, these could be found on mechas also if they have a compact cooling system.
Since the ability to manufacture composite armors is not there I do have an alternative. The chassis of the tank itself would be made of steel, titanium, or high grade aluminum similar to that of the M109 paladin whichever is available.
Over top of the chassis would be plating of alternating layers of stainless steel composite metal foam, and steel RHA. stainless steel coposite metal foam is made by literally adding tiny hollow air filled metal spheres into molten stainless steel to create a foam, The material is extremely light and has a composition of 60-70% air. It can resist 800 degrees celsius of heat for over 30 minutes. It has high ballistic resistance, a single inch of this material can obliterate an incoming 7.62x45mm armor piercing round to dust with only a 8mm indentation in the backing. it also has a high resistance to radiation. The RHA will be there as extra reinforcement against kinetic projectiles. This lighter armor will allow you to place more armor without adding too much extra weight. The fact that the tank has no emissions reduces the need for vents in the back allowing the rear armor to be just as thick as the frontal. The bottom of the hull would be V-shaped to deflect mine blasts. The inside of the hull would be lined with kevlar or ballistic nylon to prevent shrapnel and spalling. The hull would also include a faraday cage of copper wire to protect against EMP. The tank would have armored skirts that are lower to the ground than normal. If you wanted to up armor the tank you could add porcelain panels over top to absorb impact. All viewports are made of nanocellulose, a plant derived polymer that is transparent, stronger than steel, and stiffer than kevlar.
The turret ring would be made of steel and driven by two electric motors using gears with pneumatic assistance. The ring itself would be coated in copper or a similar conductor to allow for power transfer between the turret and hull to allow for redundancy if the capacitor bank in the turret is rendered unusable. The turret is attached to the hull via magnetic seal to prevent it from popping off if lifted by a mecha.
The main gun would be a 90mm coilgun. Coilguns are very reliable and they do not contain many moving parts. It would be about the same velocity or slightly faster than a standard 90mm cannon similar to that mounted on the M36 jackson. They are quite easy to manufacture as to the fact that handheld versions capable of killing small game and unarmored humans along with even semi and full auto versions are made by hobbyists from household parts. The guns themselves are much more efficient than railguns and do not have the problems of barrel wear and dont generate as much waste heat. They have no muzzle flash or report, and have much lower recoil than conventional cannons. There is a recoil absorption spring located behind the gun. The weapon is much more accurate than normal weapons due to the fact that the magnetic field keeps the projectile in the center of the barrel at all times without it bouncing around like in a normal weapon. The barrel itself is smoothbore, and the rounds are fin stabilized. The gun itself can be gyroscopically stabilized allowing it to fire on the move by taking a gyroscopic stabilization system from a mecha. It would have a coaxial 40mm cannon also taken from a mecha. A ballistic computer and laser rangefinder can also be taken from a mecha. Parabolic microphones taken from a mecha are hardwired to the computer so that they can hear the trajectories of incoming rounds and within a few seconds triangulate the position of where they came from. It also has 1-60x variable zoom optic for the gunner's sight, along with a thermal camera and laser rangefinder taken from a mecha. The tank can also have multiple video cameras dispersed around the hull to allow for improved situational awareness by the crew. The gun's ammo would be cheap to manufacture because it consists of mostly ferromagnetic metal slugs, or other ammo types with ferromagnetic sabots. The ammunition would have no propellant so it wouldn't be volatile unless you are carrying HE or HEAT, and has no casing so it weighs less and you can carry more of it. If the coils of the gun are properly insulated it could be fired underwater.
There is a crew of four men, a commander, gunner, driver, and a loader. The gunner and loader are in the turret, along with the commander. The driver is seated in the front of the hull. The extra space in the hull can be used to carry troops if you add a rear door, or it can carry extra ammo, and can serve as an impromptu living area for the crew. If you do not want to have to recharge your tank you can mount whatever magical powersource the mechas are using. It will have a hydraulically operated retactable bulldozer to steamroll the mechas.
The tank will weigh in the 30 to 40 ton range. Its profile will be made slightly narrower than a normal tank to be able to traverse the narrow roads in this semi medieval setting.
this tank due to its quiet nature would be perfect for hit and run attacks against mechas from long range, even if a shell does not penetrate a mecha it will knock it over due to the high center of gravity, and could possibly deal with a noble. In a close battle this tank will have the distinct advantage that the small mechas won't be able to harm it unless they score a very lucky hit.
Even if the nobles show up to battle, they may have a tough time fighting this thing because they will probably be using samurai syle tactics which are obsolete compared to the combined arms employed by the rebels.
Cheers :) enjoy my design before the engineers come and overanalyze it with pitchforks and torches.