Rather than use a test light at the source, use a volt meter (digital if you have one) and take an actual reading. If the source is less than 12 volts then perhaps it is enough to power the test light but maybe not enough to run the LED??? I dunno if this makes sense, but I am trying to ascertain a possible answer from the facts you provide.
Sold the TC, previous owner of 2 NorthStar pop-ups & 2 Northstar Arrows...still have the truck:
2005 Dodge 3500 SRW, Qcab long bed, NV-6500, diesel, 4WD, Helwig, 9000XL,
Nitto 285/70/17 Terra Grapplers, Honda eu3000Is, custom overload spring perch spacers.