Tug Connection
seems like this is a bit of a grey area....i myself have been on a push back with engines running.....have disconected tug taken out bypass pin....then aircraft has had a tech problem...we have then put pin back in and reconected tug and brought plane back on stand with engines running so it could have ground power/fep and a chat with ground engineer.
also a few years ago we used to meet an electra on the taxiway with the tug and bar...it kept one engine running while we pushed it backwards onto the stand.