Here's how your gate works. The gate is physically part of the gate relay under the playfield such that when the gate relay is energized, the gate opens and when not energized, the gate is spring-biased to close.
Your gate relay coil is working because you see the gate opening; it is just closing prematurely as noted above.
I've attached a bit of the schematic. The yellow path is how the relay (and thus gate) energizes. The green path is what holds it in the energized position and where your problem lies. When either of the 2 green highlighted switches open, the "hold" circuit opens and the coil de-energizes.
Your problem is either #1) the normally closed trough switch is not closed or is closed but dirty (i.e. it thinks the ball has drained and therefore it releases the gate relay) and/or #2) the normally open hold switch on the gate relay itself is not closing when the relay energizes or it is dirty.
@ArcadeTechGW suspected option #2 above.
Switch #1 is a normally closed switch at the trough with an orange-black wire at the solder tab and a yellow wire at solder tab. Switch #2 is a normally open switch on the gate relay and has an orange-black wire and yellow-black wire.
Inspect the mechanical openings and closings of the two switches: power off game; raise playfield. Look at #1 - is it normally closed with enough bias to keep it closed? Does it open when a ball enters the tough? Look at #2 while you manually pull in the gate relay actuator - is it closing when you manually pull the actuator in?
Even if both switches close, they also need to be clean to function as closed. You can clean the switch contacts with some fine sandpaper and adjust the contact blades with needle nose pliers or with a small screwdriver. Always adjust switch blades by bending them at their base. But as
@ArcadeTechGW suggests, you should own the proper tools.
Let us know how it goes. You are lucky - these switches are relatively easy to access and see. Much better than working in the bottom panel or at the score motor.
