Logging PIC for FAA on EASA TMG

[Zonkor]

While updating my log book, another question popped up for the legal connoisseurs. ;-)

I have an FAA PPL (ASEL) and an EASA PPL (SEP).

Can I log dual training (for EASA TMG rating) received on a TMG (Super Dimona HK-36, G-reg., not N-reg.) as PIC time under FAA regulations? I believe the Super Dimona counts as ASEL under FAA.

Under EASA / CAA regulations I can only log it as Dual, right?

Thanks!

[Zonkor]

Actually, the whole thing is a bit more complicated. It's already ambiguous what the FAA category of the Diamond Super Dimona is.

A search in the FAA registry shows that the few Dimonas either belong to "Glider" or "Fixed Wing Single-Engine" [1]. The several "Glider" ones are "Type Certificated" and the single "Fixed Wing Single-Engine" is an "Amateur" aircraft.

[1] FAA Registry - Aircraft - Make / Model Inquiry

So again things brings it down to the two questions:

The Dimona I flew was a G-registered (EASA-)aircraft.

1) Would I legally be able to fly it with my FAA PPL ASEL certificate from the perspective of the FAA?

2) Would I legally be able to fly it with my FAA PPL ASEL certificate in the UK from the perspective of the CAA? (Probably not relevant with respect to PIC logging in FAR 61.59.)