: So here a few more details I found out:
: The number at the bottom lugs - the model number - is: 73623
: The number at the top lugs - the serial number - is: 173984

: And as I already mentioned the movement is a Lemania 7736.

Thanks Philipp.

That clears one thing up - the 7736 is a Valjoux movement, rather than a Lemania.

And the serial number puts it pretty much smack bang in the middle of the 1969-71 timescale I surmised in my original post.

The serial number fits in precisely with Heuer's numbering schematic for other 7736-powered watches:

73623

The 736 indicates the movement that is inside the watch - in this case, the Valjoux 7736. Heuer was also using the 7733 (two registers) and 7734 (two registers with date), all following on from the 7730, which itself was a lightly remodelled Venus 188!! The world of watch movements can be a confusing one, but it's often interesting too.

The 3 indicates that the case is steel, rather than gold (8) or gold-plated (5).

And the 2 indicates what series the watch belongs to. If your watch had been a Carrera, this number would have been 5, for example. The catalogue page below shows some of the other Heuer 7736 watches:

The fourth watch from the left in this photo below is my 73655 Carrera - a 7736-powered Carrera, but in a gold-plated case and with champagne dial:

Now, the series number used on the watches I linked originally is also 2, so this ties in with my initial feeling that this was indeed the case style used on your watch:

So it looks as if your watch may indeed be a Valjoux 7736 version of these 7733 watches that we were previously unaware of, but I need to do some more digging around price lists and things to be sure. As mentioned below, Heuer was making similar watches for other manufacturers as well and it would be interesting to know what model reference those watches have.