I have a 1963 Royal Ace, (small badge, blue pearl) which was purchased secondhand with an Ajax kit in the late 1960s and indeed, the parallel action throw not properly locking into the 'on' position was, for a long time, a frustrating factor, which meant the drum was soon retired from use.
I still have the drum however and recently had another go at trying to solve the problem and.. I think I finally have done so! Here is my solution:
With the top/batter head removed, there is easy access to the parallel action mechanism and you need to to look for the angle of the pair of curved metal locators which are sandwiched between the inner shell and the parallel mechanism.
The curved metal locators have white plastic rollers on the ends, which roll against the rotatable plastic 'wedges' on each end of the square metal upper beam to enable the 'on' and 'off' throw positions.
I found that the curved metal locators in my drum had slipped upwards and each was resting against the upper counter hoop, causing a position mis-match between each wedge and roller, and therefore no firm 'click' when throwing the snare on and off.
After literally decades of head scratching, I finally tried gently-but-firmly pushing each curved metal locator, in a downward direction and from the base of each, until the semi-coils were at a 90 degree angle to the upper head. This resulted in the snare throw engaging properly, for what seemed like the first time ever!
There is also a small single crosshead screw on the outside of the shell at each end of the mechanism, which can be used to gently tighten the whole mechanism and hold the 90 degree position, once obtained.
Hope this helps!