From the early '60s thru the mid-70s at least, the Ector Co. Sheriff's Office in Odessa used Buick Electras and LeSabres for their patrol vehicles. That was because longtime sheriff "Slim" Gabrel liked the luxury of the Buicks, and the commissioners went along with what Slim wanted. But because of their resale value you didn't see much in the way of emergency equipment. These cars were equipped with red bumper lights and Federal 28 sirens underhood. It wouldn't be until the late '70s or maybe even early '80s once Slim had retired that the S.O. began using lightbars and electronic sirens.
Ditto for Midland County. The late Ed (Big Ed) Darnell was sheriff in Midland County for more than 40 years when he finally decided to retire in the mid-70s. Big Ed loved the luxury of the big Chryslers, so at the very least, he drove a Chrysler Newport. His car would have red bumper lights but no siren. The last cars to even have sirens under his administration were a pair of 1960 Ford sedans that had red bumper lights and Federal 28 sirens underhood. From that point on until Darnell retired, no Midland S.O. unit had a siren. One weekend when I was home from Texas Tech I happened to be listening to my scanner, and an S.O. unit was trying to respond on a domestic call. Apparently he got bogged down at a particular intersection because he could be heard to say, "Headquarters, call the P.D. and have them ask the unit that's in front of me to please move. I don't have a siren and he's ignoring my red lights and my horn." Another things, the Midland County units were unmarked...no signs or graphics.
Darnell was replaced by Dallas Smith, a former DPS officer. One of the first things he did was to equip all the units with lightbars and sirens, and each car had appropriate graphics. Like the old saying...."they've come a long way, baby!"