03 5.3 oil pressure drops when towing

[dbstepside]

the title sort of explains it, but here goes. i have an 03 z71 with a 5.3. whenever i tow something my oil pressure will drop slowly to the point that the warning buzzer and message come on. truck will not do it unless it is towing. i have looked at all the videos on youtube about the oil sending unit and the oil pump itself but my problem only arises when i tow something. it normally only starts once the trans kicks down and then shifts back into a higher gear. i keep suspecting the pump but hate to change it out since it wont do this at all under daily driving conditions, but i do have have to fix it my problem, as going to haul a truck 3 hours this coming weekend to a show. also i can shut truck off once all alarms come on and the problem will go away until it kicks downs again. thanks in advance for any help and sorry for the long post.