OK upon doing some further research, it appears the Frigate Southampton had a busy career. It was active in the French revolutionary wars, taking part in the battle of the 'Glorious 1st of June' in 1794, as well as the second battle of Cape St. Vincent in August, 1797. It was then 'paid off" a few months later.
So if I understand Naval service correctly, during that time period a Seamen who enlisted stayed with that ship until it was 'paid off', at which time he was free to leave the service if he so desired. So my ancestor presumably served on the Southampton from 1793-1797? Any Naval experts out there that can offer any more information? Would their have been any time off for leave during that period? Would sailors have been able to return home at all during that time?
I must say I am quite surprised to find this incidence of Naval service for this ancestor, if indeed it is actually my relative at all. I am certain that this ancestor served in the Aberdeen Militia as he is listed on later muster rolls for 1803 and 1810. But I am still a bit skeptical that this could be the same William Jaffray, since he is born and resident quite a ways inland from the coast.
I see that there are other records that may possibly refer to the same person in the Lists of Royal Navy service awards, but as I dont have a subscription to ancestry it will have to wait till I can get to the library.
Oh Well, you never know what you will find in this hobby!