Use John Philip Sousa... (I like "Stars & Stripes Forever" personally, but do ignore the rallentando going into the third repeat of the first strain!)
If you've any exposure to him you can probably hit 120 beats per minute to within +/- 10; if you've any musical training that's closer to +/-2 bpm. Let's assume +/- 6bpm, because I don't know you. That's an error of one part in twenty.
...to calibrate a pendulum's length...
Holding the top with one hand, occasionally giving it a kick at the bottom of its swing to keep it going--pushing it at the bottom will perturb its timing the least. Once you've got the length marked out of a 120bpm pendulum, go ahead and rest your arms a moment while gathering material for the next part.
...to calibrate a sundial.
Quadruple the length of your pendulum--doubling its period--and hang it from some improvised frame. Within seated arm's reach of your new grandfather clock erect your gnomon, mark your starting point, and start your grandfather clock. (Remember to give it it's kick at the bottom--not like pushing kids on the swing.) Make a tick somewhere every 60 (or 100, if you're ambitious) ~seconds~ and after 60 (or 36) ticks mark the end of the hour at the shadow's tip. And do it again. And again. (Counting this many beats is do-able, but it takes discipline. Again, you'll be in good shape if you've some musical training. Particularly if you've been a brass player in an orchestra--plenty of hundred-plus measure rests in that repertoire!*)
Build yourself a bevel gauge and mark out eight times your three-hour count. There's your Earth-day. Now in 346 of those (allowing for the one part in twenty error) go to your gate location prepared for, at most, a nineteen-day wait.
It's better than heartrate because that can be soooo variable. As a runner I know that my resting rate may be as low as the 40s, but on a stressful (Earth) day my resting rate might be nearing 60. +/- one part in five is no good. Even at the bad end of the tempo-range you'd be hitting one part in twelve.
It's better than sleep cycles because we're actually diphasic sleepers: in darkness we can easily sleep three or four hours then come wide awake, feeling refreshed as after a full night's sleep, only to re-tire an hour or two later. That's in our preferred environment, when well-fed. Throw hunger, stress, and unnatural stimuli into it and I don't think you're going to get one part in twenty accuracy.
* - Much rarer, but better-equipped for this particular exercise, are change ringers. They'll stand upright for nigh-four hours one morning, pulling rhythmically and counting their way through the 5040 permutations of their band's bells; have lunch; and do it all again in a different order in the afternoon!