Transistor that drives it.

LTG : )

It's not the diode. If it doesn't energize until a game is started sounds like the flipper contacts are closed or a logic problem. Some games (not sure on TSPP) have two sets of contacts on the flipper button. One for the lower flipper and one for the upper. I'd check that first.

Yep this is likely it. You can verify in switch test in diags menu if the button is seen as pressed or not then look at the switch inside the cabinet. May need a very slight bend to be less sensitive.

Not a transistor that drives it since that would show up on power on rather than game start.

There are two sets of switches on the right side (I think only one on the left). However, the inner switch controls BOTH the upper playfield right flipper and the "middle" right flipper near Bart. One would suspect that a stuck inner switch would fire both of them. But this is pretty easy to test in diagnostics.

Your problem is likely a switch problem as suggested by dasmb.

If the flipper does NOT energize on it's own in attract mode, it's probably NOT the transistor that drives the flipper coil. A shorted transistor would usually energize as soon as you flip power on for the game.

Reason I mention this is because this exact thing happened to an upper right TSPP flipper I fixed for a friend. The cheap ass 22NE10L transistors that Stern used shorts and fries the coil quite often.

All 22NE10L flipper transistors should be upgraded to IRL540N transistors in Stern White Star games. Terry has them for $2.95

The 22NE10L transistor was never designed to handle the currents that go through a Stern flipper pinball coil.