One would need to have several months' worth of figures to...

One would need to have several months' worth of figures to determine what happens to an individual share on changes of ratio. Some ratios change very slowly, others are much more volatile. One would need to tailor make the possible buy or sell signal to the individual stock.
On the other hand if one were to do it for a class of shares - let's say 20 companies - you may have a signal to move into those shares as a whole. If the average ratio were say 1.25 at the time you were interested, having moved up from .8 for example, and the particular company you were interested had moved up to 1.75, it would be a relatively safe indicator to buy.
It needs testing.