So, I don't really know the context of the use of this tactic by Caesar, but it certainly wasn't new or innovative. It had been known to the Greeks for centuries. Indeed, Caesar was an avid reader of the Greek general-philosopher-historian Xenophon (c. 430-355 BC) and if he did indeed use it at Pharsalos, that may well be where he got the idea for this kind of force.

The earliest (probable) evidence we have for light infantry fighting with horses comes from Sicily, around 480 BC (the time of Thermopylai). Herodotos records that the army of the tyrant Gelon of Syracuse included 2000 archers, 2000 slingers and 2000 hippodromoi psiloi ("light horse runners", Hdt. 7.158.4). Now, there is a lot of debate over whether these are in fact light cavalry or light infantry, but they fit with a wider pattern in ancient warfare of infantry that serves specifically to support cavalry in battle.

This troop type later becomes a particular feature of the Theban levy in mainland Greece. Already in 418 BC, we are told that the army they sent in support of the Spartand at Mantineia contained 500 hamippoi - the technical term for this kind of light-armed warrior. The name seems to suggest that they accompanied horses, and in fact we have vase paintings of men running along with horsemen by holding on to the horse's tail. This is exactly the kind of fighting style Caesar describes for the Germanic horse runners.

By the 4th century BC, Greek tactical thinkers appear to have realised the merit of these hamippoi as a supporting force. Their basic function was to support the cavalry by screening their movements, protecting the horses, and taking advantage of the enemy's fear and confusion as they came under cavalry attack. It is not clear exactly how these hamippoi increased the staying power of cavalry (or how they kept up with them), but we know that by the middle of the 4th century BC their use was recommended. Xenophon claims that the Thebans made good use of them against the Spartans at the second battle of Mantineia (362 BC) and urges the Athenians to recruit their own corps of hamippoi to stand a better chance in war against their Theban neighbours (Hipparchikos 5.13). Nicholas Sekunda has suggested (though I don't think this is very plausible) that the enigmatic Spartan special force called the Skiritai were a force of hamippoi.

These troops are a sign of a more general truth of ancient mounted warfare, which is that it seems to have been more effective when mounted troops and light infantry worked together. It is a common feature of Greek warfare for an attack to feature successive waves of cavalry, light infantry, and hoplites. The idea was for the first wave to be bolstered and made more aggressive by the knowledge that others would follow, and for enemies to be intimidated by the knowledge that if they stood their ground against the first wave, the next one would soon overwhelm them. Successive attacks of this kind (what I've called a "cascading charge") were practically never successfully resisted. The use of regular corps of hamippoi enabled a cavalry force to commit to charges of this kind at any moment.

In short, what Caesar describes was a common tactic among the Classical Greeks, possibly pioneered in Sicily but soon brought to the Greek mainland. If it is true that Caesar adopted it himself, it is possible that he was inspired by Xenophon, but it is likely that the tactic was separately developed by the Germanic tribes in his account of his earlier wars.

Edit: corrections