If they're actually drowned there will be mercury in the lungs, because drowning, in general, is the inhalation of a liquid (though the term is occasionally used, loosely, for inhalation of heavier-than-air gasses).
Even if the mercury golem is able to reclaim the mercury that was forced into the victim's lungs, the "losses" will be detectable as traces in the bottoms of alveoli, caught on bronchial cilia, and so forth.
Even if the victims were suffocated without the mercury entering their lungs, any metals on their person will have been attacked by the mercury, which aggressively forms an amalgam with any metal that isn't protected by a fairly heavy oxide coating. Anodized aluminum is protected, but if there's a scratch or dent that penetrates the anodize, the aluminum will be attacked vigorously where at that point. Gold, silver, copper jewelry will take on the appearance of silver (old school trick, back when students were allowed to handle mercury, was to make "silver pennies" by cleaning them well and then dipping them into mercury).
Metals frames for glasses will be attacked where the lacquer coating is worn off (along the temples, first, then where the frame touches cheeks, nose, or brow), a metal wristwatch band (even stainless steel) will be attacked, though less visibly so, as will the case of the watch itself. Keys in a pocket will be coated with amalgam, unless they're aluminum, then they'll break down completely (look for YouTube videos on mercury attacking aluminum).
You should also consider what your mercury golem weighs. Mercury is about 13.5 times as dense as water, meaning a mercury golem the same size as a human would weigh around a tonne and a quarter. Floors can take a lot of distributed weight -- upright freezers can weigh half a tonne when full, and are probably the heaviest thing, per square meter, you'd have in your house; your mercury golem weighs more than twice that, and stands on (again, assuming similar overall shape to a human) less than a quarter the area. You're likely to find structural damage to floors and joists where the golem has walked or stood.