I would start by looking up the specs on the bulb and rotating light, or better yet, just connect them through an amp meter to a battery and see how much they draw.
I'm going to guess its more than 5A on startup.
Most of those use a standard 1156 automotive bulb, these are rated at 27W at 12V, that's over 2A.
Both the motor and bulb have really big initial currents, take a look at this for incandescent bulbs starting up:
Yes, a 2A bulb can draw over 20A when it starts.
Add in the motor - especially when it starts - and you are likely to see way over 5A.
A really big capacitor across the power line After the micro-controller might get you past the start up. A few thousand uf at least.
The other solution is to support the micro-controller when the light turns on. Add a diode before the micro-controller and a good sized cap after the diode, 500uf or more.
This gives the micro power even in the main buss drops.
You might want to see what your micro-controller brown out voltage is and if its adjustable.
Other notes:
The sudden surge might be overtaxing your power supply, try a different brand.
Add in in-rush limiter to the light to keep the initial current lower.
Replace the incandescent bulb with an LED model.
Get rid of the motor and incandescent bulb, just use some bright LEDs and let the micro-controller make it look like its spinning.