The only time I've been successful in guessing a gate has been one particular routing which tends not to get substituted too often.

One 767 operates EDI-LHR-IST-LHR-EDI each day. Given there's only seven jets, and they all have other schedules (most start the day at LHR), this is a pretty consistent pattern once a 767 is assigned it.

For the morning EDI-LHR, it tends to be assigned the only large, domestic gate at T5 North. More often than not, BA676 departs to Istanbul from there. Inbound can arrive multiple places (I've done BA677 to both T5C and T5B, so the rule is definitely a random walk!).

Fat lot of good for your scenario - but nerdy fact