Can you add a separate switch (different light) to a 4 way switch?
I think I connected it to a traveler.

That is the key right there. If you pulled power from a traveler then the new light will only work ~ 1/2 the time, depending on the position of the switches.

Keep in mind with any solution that you may need a larger box to install a 2nd switch due to box fill requirements.

There are 3 possible solutions:


Switch at the source of power


Power typically takes one of two paths:


Panel -> Switch 1 -> Switch 2 -> Switch 3...n -> Lights
Panel -> Lights -> Switch 1 -> Switch 2 -> Switch 3...n


If you have the first setup then you can pull power from the always hot at Switch 1. You can't get it anywhere else because everywhere else is either traveler or switched hot.

If you have the second setup then you can pull power at the light fixture, but that would typically require running a new cable to get to the new switch.


New cable


You can run a new cable from the panel or some other always hot location to the same box that has one of the existing switches. You must pull hot &amp; neutral together - you can't piggyback on another neutral even if it is part of the same circuit (breaker), and you must make sure that the neutrals don't get mixed up in the switch box.


Smart switches


You can replace the existing switches with smart switches that only need one wire instead of two travelers, freeing up a traveler to be used to power another set of switch(es)/lights. That works because smart switches use some variant of power line signaling or wireless signaling to do their job. No new wires to run, but more equipment costs, unless you were considering moving to smart switches anyway.