See?! Yak knew angry pony could be friendly if he tried.  
…So you say but you might be the only one to think that.
 

 
I was super inspired by one of DrWolf’s anger management video to ship these two.
 
As for their ages, for some reason I can’t help but think of Prince Rutherford as an older guy, like in his late 40’s while Neighsay is in his mid 50’s. Rutherford doesn’t act like a kid or even a young adult. He’s a stubborn and loud old man who has ruled over his kingdom for decades. His focus has been on ruling so he never bothered to change his title. He was then invited to a dignitary dinner, where he met up with the Chancellor.
 
{Note, I don’t subscribe to season 8, since I haven’t even watched it yet but I like Neighsay, so he stays.)
 
As expected, they don’t get along since Neighsay is kind of a bigot. Despite his jabs at the prince for his strange way of talking or clumsy nature, Rutherford doesn’t let it get to him until Neighsay starts talking shit about his subjects. At that point, Rutherford calls him out of how rude he’s been since he arrived and that perhaps he should think about which of them is the ignorant one. Turns out his time with Pinkie and Twilight has taught Rutherford when and where to explode.
 
Neighsay, not wanting to be looked down upon, sought out the advice from Twilight, since he was sure she would understand him. She called him a jackass and told him he should at least apologize for being rude. He was still reluctant. Seeing her words hadn’t gotten through, she suggested he take some anger management, since he wouldn’t fare well with other creatures if he kept on acting the way he did. He went along with it because 1:Twilight was a princess, 2: he was noticing that he was being shunned and 3: he was sure it would just prove he was right.
 
Spoiler: He wasn’t.
 
He was told he was a control freak with deep set fears of those outside of Equestria. While he acknowledged the changes, he couldn’t help but be scared and lashed out. He was advised to make a non-pony friend and try to work through it. The doctor suggested one of his former patients, who just so happened to be a non-pony. Shocker of shock, it was Prince Rutherford.
 
At first, they were awkward, since Neighsay refused to apologies but Rutherford helped him work through his frustrations the way only a yak would. Smashing things. While Neighsay found the act barbaric, he couldn’t deny it was a great stress reliever. After a while, he took after Rutherford, shouting out his inner most frustrations and letting it out rather than burying it under a veneer of politeness. For the first time in years, he felt content and happy.
 
Ponies seeing the stallion were shocked to see the usually sour faced pony smiling and generally chipper (as much as he could be) and asked about it. He refused to tell. He eventually began to fear the end of his and Rutherford’s time together but was told that even if he was less of an ass, they could still spend time together.
 
TLDR: I ship this sour faced old man with slightly younger old man.