Could it be that the EOS switch is shorted so the low power left flipper winding is never getting switched in? That would put a heavy current draw on the transformer which might drop all of the output voltages.

Does the right flipper cause the GI to flicker at all? That would be the the high current draw for the fraction of a second after the flipper activates until the EOS switch opens.

/Mark

If you short the right flipper EOS switch with an alligator clip jumper do you get the lights to dim the same way as the left flipper is doing? That might help confirm or dismiss the shorted EOS switch theory.

Don't keep either flipper on too long though. The high power coil can overheat very quickly.

There are a few ways to identify or confirm which lugs are which like:
- the two lugs with thicker (lower gauge) wire are for the high power coil
- the two lugs with thinner (higher gauge) wire are for the low power coil
- the lug with two wires around it connects to both coils
- the two lugs that measure the lowest resistance (when disconnected from the game) are for the high power coil
- the two lugs that measure the intermediate resistance are for the low power coil
- the two lugs that measure the highest resistance are for both coils
etc...

A normally closed EOS switch should be wired across the low power coil to bypass it until the flipper has traveled through its full swing.

Details and photos at https://www.funwithpinball.com/learn/flippers-coils-and-power

Switching wires back and forth and trial and error is one way to go. Or you can have a look at the schematic try to understand how it should be wired.
Old Chicago Flippers (resized).jpg
The solder lug on one end of the high power flipper solenoid winding should have a single (black-yellow/83 or orange-black/78) wire on it directly from the flipper button. The lug between the windings should have a single short wire of unknown color (-J- is for jumper) to one side of the EOS switch. The low power winding lug will have some number of red/10 wires tied to it in addition to the other end of the EOS switch.

On the schematic the high power winding is the lower one, which is always active when the flipper button is closed. The low power winding is the other one that can be bypassed if the EOS switch is closed.