As for how they got in contact, I'd assume Myrkul reached out to him, since I would think communicating with a spirit would be a fairly easy thing for Myrkul himself. Why he picked Kethric specifically I don't think matters too much since he clearly wanted a general for the Absolute's forces and Kethric fit that description. In fact Kethric is probably a better choice than some necromancer with a lust for power because its far easier to be sure of his loyalty and that he won't pull some kind of betrayal for more power.
It kinda makes sense, if you really want to justify larian decisions and assume stuff, but at the same time - it doesn't.
It all has to do with souls, and Gods, who are EXTREMELLY petty, greedy and jealous for them, even more so than Demons and Devils. Gods only care about HOW MANY people worship them, and have complete disregard for those who do not, especially the Evil Gods.
Yes, communicating with a spirit is easy for Myrkul, but Ketheric wasn't a spirit, he died, and his soul was supposed to be taken by Shar to her domain, and she would never EVER allow another God to just take him.
OK - let's assume Shar never cared to take Ketheric (there's a book describing how Lady of Loss sometimes abandons her worshippers for lols), and he was wandering Kelemvor's domain, never receiving judgement, so Myrkul took him in. Still my question is valid - 1. Why him? He's a failure. Myrkul immediately abandons Ketheric after we kick his ass in Moonrise, Evil Gods have 0 tolerance for failure. 2. After 100 years wandering on Fugue plane, Ketheric would most likely be approached by Devils or Demons, to "save" him from oblivion (cos that is the fate of unclaimed souls) and send him to Blood War, bcos of his military experience.
But we are going too deep into nerdy stuff, long story short - what Larian did doesn't make sense for anyone who is familiar with Lore and DnD Canon.