One of my character ideas involves a Gnomish Unchained Summoner who rides on the back of his Eidolon, who would be an Inevitable. As the Inevitable only has the biped base form, it does not qualify for the Mount evolution, that turns it into a combat trained mount. What I want to know is, do the rules as written allow you to ride a friendly creature such as an eidolon, even if they are not mount trained? Do you need a specific type of saddle? Do you need to make Ride checks because you can communicate with them?
There is at least one known inevitable that is four-legged, the Zelekhut. You could discuss the possibility of using that to allow an exception to your character.
Other than that, you can normally ride a creature that is two categories larger without penalty. Like a halfling (small) on a silverback gorilla (large).
To answer your question. You only need a Ride check if you want to use the Ride rules. If all you care about is a mount to move around, you dont need a Ride check. But if your mount gets attacked, you may drop off him.
As for communication, an intelligent mount allows you to ignore handle animal checks to explain what he should do, though you still need those checks if you want him to perform specific tricks, they just dont need to learn tricks. But Ride checks are necessary if both of you want to attack together and everything else covered on Ride skill. A dragon cant breath while a mounted knight is attacking people, he has to actually choose what to do on his actions.
Alternativelly, you could verbally communicate with your eidolon to tell him where to move, that obviously wouldnt require Ride checks, but he may not take the exact route you want him to if the eidolon is GM controlled (his right, you cant argue if he chooses to). Then, you could freely use both hands without guiding him manually.
You would still require Ride checks to stay in the saddle if either of you get attacked, to get cover if you are attacked, fast mount/dismount, spur mount (because you technically makes him move faster than what is allowed by his movement speed). And to make a mount jump aswell, but not to see how far it jumps, just to see if you dont fall during the jump. Everything else (guide with kees, control in battle, fight while mounted) could be ignored by communicating with your eidolon and no Ride check would be required.