Look into the 1284x key - it's used by the majority of police cars in the US , and you can easily find it on ebay for super cheap. Once you get one, you can get it copied at a hardware store and hand them out to comrades before protests.
Here's a talk discussing things that are commonly keyed, it's very good and definitely worth your time to watch https://www.youtube.com/watch?v=a9b9IYqsb_U (I was planning to make this post today but u/alfrednobel already posted the same talk lol, guess we had the same idea)
Other keys to look into would be the ones to doorking systems for apartment buildings - those boxes that let you buzz in to go inside. They have common maintenance keys, and with that key and a piece of wire you can let yourself into the building if you need to hide out for a while. These are the 16120 and 222343 keys. Again, watch the talk, it goes into this.
Stay safe comrades!
According to Lenco, manufacturers of armored vehicles including the Bear and BearCat, manuals are limited to customers only.
However, a quick DuckDuckGo search of "site:lencoarmor.com filetype:pdf" yields:
https://www.lencoarmor.com/wp-content/uploads/2017/11/Lenco-2008-12-Parts-Catalog1.pdf
https://www.lencoarmor.com/wp-content/uploads/2017/11/BearCat_Operators_Manual_06-07.pdf
https://www.lencoarmor.com/wp-content/uploads/2017/11/2016-Lenco-BearCat-Manual_em.pdf
https://www.lencoarmor.com/wp-content/uploads/2017/10/BC-Pricelist-7-19-17.pdf
https://www.lencoarmor.com/wp-content/uploads/2017/11/Lenco-BEAR-Price-List_10-20-17-1.pdf
https://www.lencoarmor.com/wp-content/uploads/2017/11/Lenco-BEAR-Operators-Manual_em.pdf
https://www.lencoarmor.com/wp-content/uploads/2018/03/Old-new-Admin-Full-Page-FA.pdf
https://www.lencoarmor.com/wp-content/uploads/2007/12/Herald-Mail.pdf
https://www.lencoarmor.com/wp-content/uploads/2017/06/BearCat_TAC-SUV_em-17.pdf
https://www.lencoarmor.com/wp-content/uploads/2017/06/BearCat_G4_ex_em.pdf
https://www.lencoarmor.com/wp-content/uploads/2014/03/Critical-Lessons-from-Boston-Bombing.pdf
https://www.lencoarmor.com/wp-content/uploads/2019/05/A-First-Responder-Rescues-an-American-Flag-from-the-Path-of-Hurricane-Irma-on-Anniversary-of-9-11.pdf
(There are a lot more available)
Looking through the parts manual, it looks like they use a super simple door lock, similar to an RV lock, and the chassis is just a diesel Ford, so it's possible that they use that same key.
Why am I not surprised.
You posted the parts catalogue as one of the first links - that catalogue has a picture of the gas key in it. It's a shitty cam lock. Same with the door lock, as you mentioned.
And we all know what happens when you put sugar in a gas tank...............
Nothing apparently, mythbusters did the sugar in the gas tanks and it didn't work. I think just water will shut it down short term. But if you have access to the oil, just add sodium silicate and have a dead engine. It might also work in the fuel, as it's soluble in water and should get past the filter.
Edit: from the operator manual there is a water in fuel warning light "Water in Fuel: Indicates the fuel may contain water. Drain any water collected in the fuel/ water separators."
It is a diesel engine, so a 75:25 diesel:gasoline blend would fuck it up.
Also, apparently, aviation fuel will also wreck it.
Also, check out Eco Defense: A Guide to Monkeywrenching