If you look for it, there are some light strips with remarkably thin LEDs - less than 1mm thick.
As GRJ says, the wide-angle of dispersion is key for a drumhead or else you'll get a hot-spot (uneven illumination). Otherwise you have to locate the LED so far back from the drumhead as to be impractical.
Perhaps obvious, but you can carefully remove, say, the last LED from your strip closest to the end of the car. Then run a pair of fine wires from the vacant pads to the loose LED for the drumhead. In this way you don't have to find a source for quantity one LED or mess with choosing a resistor. When purchased on a strip the per-LED cost is usually just a few pennies.
