Only just got back to looking at this site but saw your query on both listings.
This machine started 'life' when it was assembled at the Coventry Works in May 1927. For some reason it didn't find an owner until about July 1929, and that was in Southampton, Hampshire. (That's what my reseaches and the registration tell me.) It was/is a Model N, which has been mentioned as an updated Model P, which is correct, for included amongst many other improvements was an oil pump within the crankcase but as this was a new thing the tank hand pump was kept so that riders could give a hand pump if they didn't trust the automatic pump. However, on this bike the oil outlet from the oil compartment in the tank is not being used (thanks for all the pictures), and a separate 1928/29 oil tank from a Model N de Luxe has been added on the saddle down-tube.
The bike was listed in the VMCC registers from 1969 and the last report I received on it was that it was seen at the Stafford Show in 2006 (presumably for sale) and was in need of restoration. Since then it has obviously been at least given a coat of paint and found its way to the US.
The 'T27' and 'T' stampings on the tappet positions of the crankcase are not original Triumph marks.
The Model R had an over-head valve engine and this is obviously a side-valver (494cc).
Model H production finished in 1924.
I have written 17 booklets covering various Triumph models and one covers the Models N and QA (Sports version of the N). The auxilliary oil tank information is included in the booklet covering the Models N de Luxe and NL, for as mentioned it was not fitted to the standard Model N. If you are interested, or anyone else who might read this, sent me an e-mail at <peter@triumph.gen.nz> The booklets cover most (still writing to fill the gaps) Triumph models from 1901 to 1934.
Peter
(Triumph specialist for the VMCC of Britain, but now resident in New Zealand)