You can test with them out of the car. The fact that it gets warm might indicate the internal coil is still good. I would have to say your injector may be stuck internally. Take a reading with an ohm meter.
I have 4 CIS CSV's. 3 for my '73.5, and 1 later. 3 of 4 click with 12v applied. 1 gives a light arc with 12v, but is stuck internally. All 4 have about 3.2 ohm resistance reading.
I had a similar issue with 2 injectors on a used '86 3.2 I rebuilt. It took me quite a few days of brake clean, pulsing them with 12v, and a bit of tapping with a rubber screwdriver handle till they freed up and starting clicking. The car ran great when I was done, and the freed up injectors worked fine.
This video shows one guys method
https://youtu.be/rUUgR94drxg?si=RfX7gV-VeORmNYSC