Are there any Jewish sources (halachic) that explicitly discuss political activism, or being involved with secular governments. The older and more primary the source(s), the better.
There are some sources from the commentaries on משנה אבות, the ones that deal with this topic of "not trusting the government".
Rambam warns on this Mishna that pursuing friendship with the authorities removes someone from the world because it consumes them, to the point that most people who do so do not escape the damage of doing so. He gives the example of Doeg who lost himself to this even when the "authority" was Shaul and Shmuel!
דרך חיים on 2:3 "ואמר הוו זהירין ברשות", "Be careful of the authorities" elaborates this for us and warns us that a politician feels superior to others, and therefore doesn't even count himself among others. This is a warning to both those who wish to seek to benefit their community through lobbying, in that they should be careful they don't become aloof like this, as well as a warning that they shouldn't put their trust in the authorities. Basically stay on your guard, and trust only in Hashem.
Yachin on 2:24 gives further warnings:
הוו זהירין ברשות הוו זהירין לבלי לבטוח בהבטחתם, לפזר להם ממון הצבור במתנות יותר מדי. גם לא תבטחו באהבתם לגלות להם עניינים, שאפשר שיזיקו לצבור עי"ז:
Be careful not to trust their promises, to waste the money of the community in distributing gifts more than necessary. Don't trust in their warm disposition, and give them information, as that may damage the public.
Note however that עיקר תוספות יום טוב on the same Mishna explains that it's a big mitzva to befriend the authorities for lobbying/activism purposes. He gives the example of Rebbi, and Mordechai, from Midrash Shemuel.
כי זו מצוה רבה היא להתודע להם כדי לפקח על עסקי צבור
As this is a great commandment to become acquainted with them in order to supervise communal matters
דרך חיים on 2:4 reminds us that looking after the needs of the community is emulating Hashem, i.e. His will is to provide every matter for the public, and therefore by doing so we are making His will our own. He tells us that we should never separate ourselves from the community in the way a politician does, even if we have to befriend the authorities.
Ultimately, it is our merit that decides our fate, not the authorities and we should put our trust in Hashem, even while we make our histadlut in doing activism. Every day, 3 times, we pray:
וּמְלוֹךְ עָלֵֽינוּ מְהֵרָה אַתָּה ה' לְבַדְּךָ
Be our Ruler speedily, You Hashem, alone.