It's not the aux lights with the relay that causes the problem (it does actually use the ignition switch for the trigger, that does add a little more to the overall), it's the headlight running through the ignition switch. Touring has one less headlight of course so problem is less, but putting it on a relay directly from the battery will brighten it considerably. That yellow tint in the headlight will disappear and become a brighter "white" light even with standard bulbs.
It's a nearly "must have" modification for Standard and Classic bikes with dual headlights. Adding anything to the load on the switch (GPS, lights, etc.) will cause the solder points in the switch to become soft due to the heat from resistance. It's the soft solder that allows the wire to vibrate loose and cause all kinds of electrical maladies, including shutting off and not starting while driving down the highway (I had that happen on more than one occasion before the problem was found and fixed). It can also cause charging problems, intermittent power loss, gauge trouble and running problems like high/low idle and missing.
If those new aux lights look brighter than the headlight, it's because of the switch, not the bulb.
