I think a big part of why Cider and Dandy work together is because Dandy does NOT care about Cider's wealth. He ran away from aristocracy in the 1800's. He's tasted wealth growing up and just how awful it made the people he trusted act with each other. He meets Cider because he sees an ad for a paid study at CiTech.
At the time, Dandy was flat broke and temporarily rooming with Dee in a rather run down apartment, and took the money so both of them could have a little more comfort. (I would also like to add that Dee trusts Dandy very much but can't help finding relief in the fact he will never remember their true face because of his memory issues.)
As soon as Cider catches the information that Dandy is the longest living human he's ever heard of, he has to meet him in person. The tests he goes through are specific to him now, to study this thing in particular. Unfortunately, the original team behind his surgeries are long gone and so is the information.
So, as Dandy is spending time in the lab with tests being run on him he begins annoying the staff to let him see Cider a little bit more. The more time they spend together the more Cider realizes Dandy likes getting a rise out of him much more than any hint of trying to get further money or status out of him. He's honest and real, and so damn annoying constantly but Cider can't help but find it refreshing. There's no lying or kissing up. Dandy even mocks the idea that Cider is anything special because he's a billionaire. He calls him 'The grand and esteemed Dr. Cider' as a joke when he requests to see him.
Cider extends the testing period and claims results were 'inconclusive' as an excuse to keep spending time together.
