I think the 15 Ohm rating is incorrect. Placing that across a light bulb (or LED) is pretty much a shunt.
Went looking at a bunch of searches and something in the 560 Ohm rating shows up all over the place. That is small enough that a light bulb in parallel could actually light up.
V=IR is the starting formula. V is Volts, I is Amperage, R is resistance. A 15 Ohm resistor on a 15V circuit is 1 amp. Watts = Volts x amps, so 15W. That is massive. A 560 Ohm resistor will only 0.4 watts. A very managable heat load to handle. Here are a couple of references to the 560 Ohm resistor.
https://www.ford-trucks.com/forums/1110224-4th-wire-on-a-1g-alternator.html
https://www.garysgaragemahal.com/#nabble-td64593
This one lists 510 Ohm
http://1969stang.com/forum/index.php?/topic/59902-1g-to-3g-alternator-conversion/
For this basic of a circuit the exact value doesn't really matter. Just anything in that range.
I did see the 15 Ohm reference on a Mustang site. No doubt you found it too. But general electronics engineering kicks in here and tells me the 500-560 is probably the right number for a safety shunt around the light bulb.