Sir deeredoctor . . . . .
Definitely a thermal inrush, current limiting thermistor that you have there . . .BUT in a very small power handling profile . . . just looking like its starting its decline, from the very first time powered up and starting a timely decline to result in a failure in a much shorter time than you would want to be expecting. With a final fracturing and a popping off / open connection of one of the solder capped leads.
From what info that you have given, looks like this would be a good fit.
https://www.mouser.com/ProductDetail/Semitec/12D2-10LC?qs=sGAEpiMZZMuBd0%2bwiCVS2waoyKMmx3l3SVq8KGWQqfw=
Only two Amellican dollah . . . a pop . . . BABYCAKES !
This prescribed unit has a multiple upsizing in the thermistor pellet, for 16x enhanced reliability factor.
I think that the units quiescent cold resistance @ 25Degs C would fall in at being 10-12 ohms and shift downward in resistance in ~ 10 seconds and then hold, with solenoid run time, continually pulling current thru it.
If you have or can get access to a laser beam thermometer, and have a good worling unit.
Do these tests:
Take a resistance reading with a DMM to get the cold resistance reading of one of the good . . . albeit . . . somewhat puny . . . .Original Equipment Manufacturer . . . . . themistors.
Watch in probing, them as they are somewhat fragile on the end caps or particularly in bending the leads.
Have a DMM connected in to be reading voltage across the good OEM thermistor, power up the solenoid and immediately take and log down the voltage being read across the implied good thermistor.
Run the activated solenoid for a 30 min to 1 hr " benchmark " test, and retake the voltage reading being across the on time activated and then warmed up thermistor . take the laser beam thermometer and shoot the peak surface temperature of the thermistor pellet.
FIO . . .
A companion unit associated with a series incandescent indicator lamp,. . .it loafs . . . would have NOWHERE near the peak power demand of a solenoid.
A continuance . . .pending feedback . . .
73's de Edd