I can’t tell from your pics, but it is almost certainly an issue with your EOS. Could be mechanical or wired incorrectly or both.

Do you have schematics? Compare them to your left and right assemblies and you should be able to see what’s going on.

When you order a new correct coil, go ahead and order flipper rebuild kits and start over with these.

Read through this thread to learn all about flippers.
https://pinside.com/pinball/forum/topic/vids-guide-to-upgradingrebuilding-flippers

I’m not recommending you upgrade, there is just a lot of good info there.

As Black_Knight said, probably wired incorrectly or misadjusted EOS switch.

Use your DMM to verify the wiring after you replace the flipper coil. When the flipper coil plunger is extended to the stop (i.e., coil energized), the EOS switch should be open and you should then measure the total resistance across both sets of windings in the coil. When the plunger is in the resting (unenergized) position, you will only measure the resistance across the low resistance winding. Verify with DMM.

Additionally, when you press the flipper button and hold it, if you hear the solenoid humming or buzzing, release the button immediately. Most likely the EOS is misadjusted. Holding for 20-30 seconds will overheat your coil.

The EOS wires should always be soldered to the terminals at the banded ends of the diodes. The power wire should also be soldered to the outer terminal at the banded end of the diode (looks to be the terminal with the brown wire in your picture). I assume the brown wire is power and the orange is return or the fuse would've blown immediately when the flipper button was pressed, so that should be correct.

As the others have said, the EOS switch is probably misadjusted or it is shorted somehow.

Directions for checking that the EoS switch is opening and functioning correctly are in post #3 above:

If you need more specific guidance on how to do this please advise.