Goes haywire seeing Trump and Vance? (4)

I believe the answer is:

egos

I'm a little stuck... Click here to teach me more about this clue!

'trump and vance?' is the definition.
I can't tell whether this definition defines the answer.

'goes haywire' is the wordplay.
'haywire' indicates an anagram.
'goes' anagrammed gives 'EGOS'.

'seeing' acts as a link.

Can you help me to learn more?

(Other definitions for egos that I've seen before include "feelings of self-importance" , "Lots of self-esteem" , "Self-images" , "People's personal pride - the parts of them that are conscious" .)

I've seen this clue in The Independent.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.