You guess right.
If all else fails one idea is to wire a resistor in parallel with the new LED bulb to increase the current. If the old bulb was, for example, 6W, that would be 0.5A at 12V.
From P = I^2 x R
R = P / I^2
R = 6W / 0.5A^2 = 24 Ohms.
You need to calculate your current from your bulb power of course.
So in this example, a 6W / 24 Ohm resistor is the target. With a power safety factor you could try these 10W parts. They do a 25 Ohm:
https://www.ebay.co.uk/itm/265460044257
The same principle is used here but these are 6 Ohms (25W) which would be 2A at 12V and is too much for an indicator:
https://www.12voltplanet.co.uk/12v-led-load-resistor.html