In the Uraguayan context, it looks like a local social reference, "pichonera" being a local hero in a (local-style) beret, as it were, "our man who wears the local garb". If this is for travel literature, it may be most effective to leave the two words in Spanish and see if it's possible to work in an explanation elsewhere. If this is for a tour guide or the prior option is not feasible, perhaps something like "local political candidates as 'our man for the job' or 'the man in the beret we all know'..." I think it needs some sort of cultural explanation and cannot be directly translated, even if the explanation is worked in elsewhere. Perhaps a Uruguay native could help distinguish further nuances or associations.

They seem to be south-american terms - I think this is a cultural reference.
I can find references to the hat being quite military, as in local political candidates wearing those hats, on that side of the politics. And then those that build or come from these bird's nests. I have read a few articles where this is used as kind of a term for very, very small houses. There's a political group in Mexico which are fighting to make them stop building such small, pokey houses (pichonera).

So your political campaigners could come from those kinds of parties, those that come from those backgrounds, or are known by those markers from the campaigns.

Indeed in this source:https://www.lofficielmexico.com/moda/la-historia-politica-de...
It says that these hats are generally associated with rebels. Perhaps a rebel or opposing political party? Those from poor/small houses and rebel oppositions? Something like this perhaps - many English articles mention Boina too so could keep it like that (Boina-sporting parties)..

https://www.unimexicali.com/noticias/bajacalifornia/articulo...
http://www.consejomexicano.org/index.php?s=contenido&id=575

I am not an expert in politics or southern america, just some things I've found and interpreted :)