OK, touch switches are very sensitive. This could be radiated noise rather than conducted noise via the power supply. Since your current draw is so low, here is how to troubleshoot. Get a nine volt transistor battery and connect this to power your circuit rather than the car battery. Keep your circuit connected to ground which is the car frame. Just connect the nine volt battery from the +12V input to your circuit and the car's frame. Start the car and see if the same problem exists. If the problem goes away, then the noise is conducted on the +12V input to your circuit. ( I am assuming that your circuit contains a linear regulator down to some lower voltage like +5V. If this is the case, then you have enough headroom to reduce the input from +12V to +9V. If you are using the +12V directly, then you may have to include two 1.5V batteries in series with the +9V.)
If the problem remains, then the noise is either radiated through the air and is being picked up by your touch plate, or the noise is being conducted through the car's frame which is the ground circuit of the electrical system. To determine which, you will be required to completely float your circuit. Completely isolate your circuit. You will probably have to replace its normal output with an LED to see what state your circuit is in. If the noise remains when completely isolated, then this is radiated noise.