Yes, I'm doing the same. If I figure anything out, I'll post it here.
GOT IT! Homelink People don't understand their own product. Once a Homelink button (these days) is synced to a receiver, it cannot be synced to another receiver using the same button. (European garage thefts prompted this a few years ago). So, completely deprogram all three buttons on your Homelink in the vehicle. Leave one button "un-programmed" to any garage door or receiver. Take a handheld remote operator and sync it first to your gate opener using the gate opener's Learn and Open button. Then, sync it to an unprogrammed button on your vehicles Homelink unit per instructions in the GX owner's manual. Last, using the "Learn" button and "open" button on the gate opener and hold down the unprogrammed Homelink button within 30 seconds AND until it begins flashing green. Works for me! Learned this with help from an Audi dealership a few years ago. You may not have to deprogram all three Homelink buttons in order to re-program one of them but whichever one you use to sync with the gate opener will no longer work to any other receiver or garage door in all likelihood. Bottom line: Homelink Buttons do more than simply send a signal these days . . . they retain information from a given receiver and will only work with that receiver.
See/read my last comment . . . issue solved. Yes, gate opener is a Liftmaster.
