I would assume a fairly simple 2-step mapped key set to trigger when the key is "pressed OR released" would do fine.

The first step would simply call the bind/macro for Gift of the Queen on your secondary character and the second step would do a "Sync Cursor Action" (Target of "All w Current" would work fine) and send your Mouse1 key.

I use something similar for some ground targetted spells. The only real difference is that I usually have the mouse sync happening in step 1, so that there are atleast a few frames between that and the actual click to make sure it has time to work. Not sure if it's really necessary though.