LED's popping fuse?

[69hugger]

I recently bought a '67 C-10 pickup with all LED lighting. The wiring is AAW, and the truck was professionally built. The license plate lights utilized those bolts with LEDs to illuminate the plate. Those LED bolts had been wrecked by the consignment dealer when they removed the old license plate. They twisted the wires, breaking & shorting them, causing blown fuses on the running light circuit. Their fix was to just cut the wiring to the bolts, and cap the brown supply wire. No more popped fuses.
Wanting to have license plate lights, I bought some new LED bolts (from Amazon), and figured I'd just replace the trashed ones. I tested them from the package, and they worked great. I then wired bullet connectors to them and the brown supply wire, soldering the wires to the bullets. Then covered all the connectors with shrink tubing.
When I plugged the lights into the wiring and pulled the parking light switch, instant popped fuse. I unplugged the lights, replaced the fuse, and tested the brown supply wire to ground, my test light worked fine, no popped fuse. I tested the LED lights again across a battery, and they worked fine.
My only theory is that the LEDs draw so little current is the circuit sees them as a dead short, popping the fuse.
I wonder if I need to wire in a resistor so there is more of a load on that circuit. If so, I have no idea that specs the resistor would need to be. Or the best place to get them.
Any electrical wizards that can either confirm my thought or give me another idea as to why these are causing blown fuses would be greatly appreciated.

As always, thanks in advance!!

Bill