Does the flash to pass only effect the right side?
No, it puts both headlights into high beam for the duration of the pressing of the switch.
The headlight/other control switch assembly should have nothing to do with the city lights (at all) They are even on different circuits. So it is likely the low-beam element has failed, or the connector/wiring to it is a little wonky, perhaps disturbed by your installation. Did you pull off the headlamp connector and move the wires and put it back on to see if it solved the problem? If not, next step is to remove the bulb and look at it to see if the element is out, or swap it with the other bulb to see if the problem moves.