Just rode HAL today with no reciprocal agreement (however a JS is always welcome on my plane if they want to go to sunny Chefornak, AK this time of year).
Gate agents will look at a list and say you're not on it... then you just ask to get approval "at captains discretion", you get a small form to fill out, intro to CA and FO, put on a smile and be courteous and respectful, CA will sign it off and on your way you go.
NOTE: Gate agent printed me a seat assignment before the CA signed off the approval, seems as though they're very open about jumpers and more of a formality than anything, though it should still be respected.