I notice this car shows up in the background of many episodes.
Was that Jack Webb's personal car or was it Marty Milner's?

Don't know about real life, but at one point I think the gold Mustang was character Pete Malloy's personal car.

Stalker car

And I've noticed that this gold Mustang seems to appear in 90% of the episodes so it makes me wonder if they are shooting the scenes on a closed space as it would not be possible for that car to be in as many scenes as it is if they were shooting in the wild.

I'm fairly certain that a MeTV promo once stated that the car belonged to Milner.

Interesting, his real-life car. So I guess both Milner and his Mustang were both stars of the show!

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That must have been a pretty popular color combination around that time. I saw on a forum that it was a 1968 Mustang. I once drove a 1970 Buick Skylark that also was gold with a white vinyl top.

Yep, gold was a big color back in the 1960s and early 1970s for cars. Along with green and brown.