[ricard]

I think you're thinking of the MP22 or one of its brethren (MP32, MP321, MP38) as seen in the first picture below. That machine is from the latter part of 1950s though, whereas the TM-311 depicted above is from 1966.

(The MP22 is indeed all-solenoid controlled, with the mechanical design similar to the Grundig TK8 and TK9 machines, with one solenoid beneath each reel holder, and one for the pinch roller, although the speed change was mechanically effected rather than electric).

At the start of the 1960s, Luxor brought out a very compact three speed chassis which they they used for a veriety of machines, en example of which is given in the middle image. However, for their simpler machines, as the 1960s progressed, they turned to using the TD2 chassis, as shown to the right. Given that they didn't seem to be doing much development when it came to mains operated machines, I'm a bit surprised that they would have made the effort to bring forth a battery operated machine, especially since they'd never made on prior to that. But given that no one seems to recognize it as being some generally available chassis, it certainly seems to be an in-house effort.