Hi Reptile, you are correct in your assumptions. The frmae number on the '65 ^T should be on the cast section of the head stock between where the down tube enters it and the top near the headstock bearing, it should start 6T DU****** as the ehgine No.
The factory did a 'repair service' where bent or damaged frames could be exchanged BUT........... This was only available to Triumph dealers AND the original number was stamped into the replacement frame BEFORE it left the service dept. The damaged frame had it's number removed and it then went into the system for repair etc.
Now, it is possible you have no number on your frame, as you correctly identified F8381 is a casting number.
Are you a member of TOMCC?(
www.tomcc.org) If so, contact the machine Registrar and he will be able to advise you on which way to proceed.
Roy.