There was originally an 8-watt lightbulb there. The wiring will support two bulbs, so that's 16 watts, or 1.3 amps at least that it will handle (if the driver's side light is off, though it will probably handle more?). So the switches are rated for at least .65 amps.

50 LEDs, 2v each is 10 rows of 5 LEDs. At 130mA for each row, that's 1300mA. Considering it's a 10% max duty cycle (per the LED specs), and there's a buffer capacitor there, the switch shouldn't see more than .65 amps, though I'm not sure how much the wire will contribute vs. the capacitor.

Also, my power supply I'm testing with only supplies 1.5A, so we'll be sure we're within the limit.

A frequency of 60 Hz, pulse width of 10%, equals 180µF burnt for each pulse. If the wire contributes half that, it's 90µF.