Trouble converting 12VDC incandescent to LED: lack of resistance
I would tackle this problem in two phases.

1) Find out the minimum resistance needed to tell the computer that the bulb is installed.  You can do this by connecting the original bulb with various resistors in series with the bulb.  Take that resistance and divide the value by two so as to have sufficient safety margin.

2) Design a circuit that has that resistor installed while 12V is not available.  That could be a small 12 Vdc relay with the resistor connected to the Normally Closed contact or it might be able to be a J-FET, depending upon the resistor value.

The idea is that the resistor tells the computer that the bulb is installed and working so that the full 12 Vdc is supplied.  When that full voltage is available, the LED consumes enough current to keep the computer happy.

We can give you better guidance once you determine that minimum resistance value.