Aircraft tow - using strobes when crossing live runway
I recently was on the brakes of an aircraft tow. Part of the tow crossed a live runway (the tractor driver was in contact with ATC). As we started to cross the live runway, I switched the strobes on until we were clear, then switched them off. After the tow I was advised by the tractor driver that strobes were not used when crossing a live runway as he was in contact with ATC. My question is - what is the correct procedure for a towing aircraft crossing a live runway with regards to using, or not, strobes?