@Dolfin
This is a very common problem that I call flipper bounce.
Flipper coils have 2 circuits. A powerful "flip" and a weaker "hold". The flip uses a large momentary current that would destroy melt/ burn out the coil if present for more than a few seconds so the hold coil uses a much lower current that is safe for extended periods.
Late 70s/ Early 80s Classic Bally flipper coils are much physically smaller and use lower voltages than the later games. As a result the Bally SS coils are relatively weak in terms of both flip and hold circuits.
The flipper EOS is normally closed meaning that current initially powers the flip coil. When the flipper is energized and the plunger pulled into the coil the EOS is opened and this switches the large flip current to the small hold current.
In order to get maximum flipper power out of these naturally weak coils you want the EOS switch closed as long as possible - but there is a trade-off of flipper bounce.
The hold coil is naturally weak. If the EOS gap is too small the ball striking the flipper tip can push the bat downwards momentarily closing the EOS. This gives a brief "flip" as the more powerful coil engages for a fraction of a second. This is what your video shows
It may be virtually impossible to completely eliminate this bounce IF you want decent flipper power on a 40 yr old machine - it is all a trade off. Especially when the game gets hot so the flippers weaken anyway and the EOS gap may reduce due to thermal expansion
There are a few places to look.
1. Most obvious is that the EOS gap is too small. Widen it and see if the problem goes away. If this is the issue - - you need to set the optimum gap through trial and error that gives good flipper power (narrow gap) whilst eliminating flipper bounce (wide gap).
2. The flipper coil may be damaged/ weak. So replace if necessary
3. The high voltage cabinet button switches may be dirty/ pitted. So clean (will require abrasive paper) or replace
4. Your power circuits/ wiring looms/ bridge rectifiers/ soldered joints are weak so can't provide enough current. You'd be very unlucky if this is the case.