Hi there! Sounds like you may have a different issue than you might expect, perhaps.
Have you ruled out the shooter lane switch as being an issue?
If the lane switch doesn't change state with a ball on it, then the lifter start relay will not disengage.
There are multiple things that could cause all the balls to lift, and I don't think I've ever seen the lifter start relay be the problem.
Here's some basic info on what should happen when you start a game:
1) All balls drop into trough
2) Trough switches (especially trough switch #8) tell the game to lift the first ball to the playfield.
3) Ball #1 is lifted, and depresses the shooter lane switch
4) Timer unit increments to position 1 (through lifter cam switches)
5) Lifter motor returns to home position, ready to lift another ball (through the lifter cam switches).
When the lifter start relay is engaged, the game cannot lift another ball if there is a ball on the shooter lane switch.
If the lifter start relay stays on, the issue is either with a magnetized plate, or with the ball gate switch. This is a normally closed switch which sits under the ball gate cover plate. Removing this allows you to see (with some difficulty) the switch. If this switch is fouled, then the lifter start will remain engaged. If this happens, then if the shooter lane switch is fouled or otherwise not changing state properly, the game will continue to lift.
Especially if the timer is not incrementing.
Bingos have a fairly sophisticated failthrough compensation system in case one of these elements fails. When multiple elements fail, interesting things can happen.
Check those things out before replacing the relay.
One last thing: on the lifter start relay, one of the switches physically closest to the coil will hold power to the relay. If that switch is stuck closed or otherwise broken, the lifter start relay would stay engaged.
If it doesn't engage at all, then the lifter would not work as you described, unless you had other issues.
My #1 suspect with lifter problems is the shooter lane switch. #2 is the gate switch #3 are the lifter cam switches.
But make sure the timer is incrementing. If not, you've got other problems.
You can check this without leaving the lifter powered. Start the game, let it lift one ball, start to lift #2 and shut the game off. Go to the back and check to see if the timer is out of 'home' position.