Our Constable was pretty laid back. He worked a full time 2nd shift job and mostly told us teenagers to quit cutting across Mildred’s yard.
I only saw him take someone into custody one time in 30 years. Keith (the constable) was standing on the sidewalk when some clown made a u-turn in the middle of the street while tipping up a 40 oz Budweiser and almost took out a little kid on his bike.
I think our constables are mostly occupied with being “officers of the court”, including serving papers and such. They drive regular ol’ cop cars and I know for a fact they can pull you over for traffic violations.
In the last TX city I lived in, we helped our constable get elected. He was there drinking with us at the party on election night. That was Bush vs. Kerry, 2004 (the last prez election that involved a celebration).