Automotive LED retrofit causing strange phenomenon
The cold resistance of a light bulb is usually far lower than it's resistance when running.  If you can find the wattage of the bulb, you can calculate the current from P/V = I and calculate the resistance needed from V/I=R

V here is 13.8 volts, P is power in watts, I is current in amps, and R is resistance in ohms

Kinda defeats the power savings of the LED lamps, and watch out that the heat from the resistor won't slowly discolor or melt the plastic.  But with the existing electronics, you have to "fool it" into thinking that the bulb is ok because it's drawing the expected current.

Option:  You COULD replace the lamp with an LED that draws the same current.
I advise if you do this, to invest in some very good sunglasses.  :)