In Season 12 (and possibly Seasons 10 or 11) Fred MacMurray is shown welcoming viewers to the show. I think he says "Welcome to Our Show." Then the opening credits are shown.

Any ideas as to why that was done?

Was there a test audience conducted which indicated favorably that they would likely continue to watch MTS with MacMurray's personal introduction vs changing the channel?

I asked the same thing about Family Affair. Here is that answer.

https://www.sitcomsonline.com/boards/showthread.php?t=414640

In Season 12 (and possibly Seasons 10 or 11) Fred MacMurray is shown welcoming viewers to the show. I think he says "Welcome to Our Show." Then the opening credits are shown.

Any ideas as to why that was done?

Was there a test audience conducted which indicated favorably that they would likely continue to watch MTS with MacMurray's personal introduction vs changing the channel?

This was probably a Fedderson trademark thing. It was done throughout the series' original run to introduce the sponsor. Starting in season 10, MacMurray filmed the alternate that did not include the sponsor, which was probably meant to be used for syndication and daytime airings. In season 10 syndication airings, the welcomes were included years ago, then in subsequent later packages, were removed. In some season 11 and 12 episodes it's randomly still included. It's unknown what the season 12 original airing openings looked like. Since the reduced-length season 12 openings shown now are grabbed from a different season, what the network airings looked like is anybody's guess.

Wasn't there an "outro" where Fred would say, "Thanks for watching. See you next week on...", and each boy would say, "My...Three...Sons," and then Tramp would bark?

Yes, I've seen that. It probably made it to 16mm copies of the original network masters. It also probably made it onto some Columbia House VHS tapes (as did the MacMurray "Welcome to our show for...")

Too bad they cut this stuff out on DVD home video.

Okay that makes sense that Fred was doing a commercial plug. I found one on y/t with the Bristol Meyers Excedrin PM. (I suppose some episodes about youth making wrong choices would cause some parents a lot of grief and lead to insomnia :)

I also saw a closing with Toni (hair dye) and Casual. Both seem to be odd choices as I think those are targeted for women consumers.

https://www.youtube.com/watch?v=1mHwu16pvZY&ab_channel=TVTA

Regarding Family Affair, I find it a little interesting that I've seen only Sebastian Cabot and child actors Johnny & Anissa doing those -- while series star Brian Keith apparently never did one (nor Kathy Garver).

Okay that makes sense that Fred was doing a commercial plug. I found one on y/t with the Bristol Meyers Excedrin PM. (I suppose some episodes about youth making wrong choices would cause some parents a lot of grief and lead to insomnia :)

I also saw a closing with Toni (hair dye) and Casual. Both seem to be odd choices as I think those are targeted for women consumers.

https://www.youtube.com/watch?v=1mHwu16pvZY&ab_channel=TVTA

The Youtube here was lifted from a Columbia House tape, from the "Who Is Sylvia?" episode from season 10. Another Columbia House tape has a rarer MacMurray opener from season 8.

A Youtube comment mentions that the correct, original season 12 opener has not been seen since the original airings, which is correct. That poster mentions that it probably included Ronne Troup and Dawn Lyn (also probablty correct), and that they are not in the closing credits. They are probably deleted (along with the rest of the main cast) in the season 12 closing credits in the films we see now. Those closing credits are sped up and the main cast are edited out, the only season to have cast edited out. This is another reason why the original network episodes need to be located, and proper TV prints need to be made.

"And now, a word from our sponsor(s).

Did those words have a name?

I wonder if they thought it rude to just send us to a commercial and not let us know that was where we were going.

I think those words suggest a product endorsement. If I think Steve (MacMurray) is worthy of admiration then I might take his word (endorsement) about using X brand for _______.

It's not a mere product endorsement, though. The sponsors in those days were producers. People with ideas for TV shows would be just as likely to go to an ad agency as to a network. The agency had TV people who would develop shows. They'd reach in one direction for a network to air it, but they'd also reach out to their clients for a sponsor to pay for it. All of these people would then be working together to fill a timeslot. So, the sponsor was endorsing the show as much as the show was promoting the sponsor.

Grant Tinker drifted from network to ad agency and back, and then on to producer. He gave a long interview to the Emmy foundation that, in part, shows how everything worked c. 1960.

https://interviews.televisionacademy.com/interviews/grant-tinker?clip=3#interview-clips

"And now, a word from our sponsor(s).

Did those words have a name?

I wonder if they thought it rude to just send us to a commercial and not let us know that was where we were going.

These are bumpers -- https://en.wikipedia.org/wiki/Bumper_(broadcasting)

They're rarely seen on TV today, other than with children's programming. But they were common in th 50s and 60s.

"Hi. Welcome to our show."

Fred MacMurray dyes... his hair! ;)