1920s radio jingles--what were they?

Okay. I have determined, through much research, that the very first radio jingle ever was a Wheaties commercial that first aired in 1926.
I don’t know if this conflicts a report that “In My Merry Oldsmobile” was used in advertising by Oldsmobile, beginning in 1904. If nobody used a jingle until 1926 then where was the Olds theme song used, up until 1926?
By “jingle” I mean a catchy rhyme set to music–a catchy tune.
What I’m really looking for, though, is the kind of jingle that might catch the attention of, and be sung by, a 5-year-old, whether appropriate or not.
If I can’t find anything else I guess it’s gonna have to be Wheaties. (This is a very, very small detail going into a historical mystery novel.)

Here’s a few paragraphs on the subject from Elizabeth McLeod written in 1999

The old Longines OTR album, with Jack Benny and others, left the impression the first (or one of the first) jingles was for Interwoven Socks with the Happiness Boys, Billy Jones and Ernie Hare. Or is this contest much like the “first radio station” depending on definitions?

The whole question of jingles is a difficult one – because jingles weren’t invented. They evolved out of theme songs during the twenties, and many of the earliest theme songs were clearly intended to advertise the sponsor’s product, even though they never mentioned the product by name. I think one of the early master strokes in this technique was the use of “Brighten The Corner Where You Are” as the theme for Harvey Hindemeyer and Earle Tuckerman, a.k.a. Goldy and Dusty, The Gold Dust Twins. The opening announcement for their WEAF/Telephone Group program clearly tied the theme song to the product, by suggesting that Gold Dust Washing Powder really did “brighten the corners.” In the same era, Harry Reser’s “Cliquot March,” introducing the Cliquot Club Eskimos, was a purely instrumental piece – but its “sparkling” banjo-driven melody was obviously intended to evoke the image of ginger ale, and it was accompanied each week by a barrage of sled-dog sound effects clearly meant to remind the audience of the company’s Eskimo Boy trademark. And what better theme song for a toothpaste program than “Smiles,” the weekly intro for Sam Lanin’s Ipana Troubadours?

There have been claims that the “Have You Tried Wheaties?” jingle was first used around 1926 on WCCO, Minneapolis, then owned by Washburn Crosby Company, the makers of that cereal, but I’ve never seen proof of that claim. By 1933, this theme was used with slightly altered lyrics, as the closing theme for “Jack Armstrong.”

As to the Oldsmobile song (Come away with me Lucille in my merry Oldsmobile). Okay, it was written by Gus Edwards and published in 1905.
It was a popular, catchy song and people bought the sheet music for it!
Writing music on commission for a commercial product wasn’t a new idea. Remember that John Phillip Sousa was paid $50 by The Washington Post newspaper to write a march for them.

There’s nothing at all contradictory about your research. NBC wasn’t founded until 1926 (and CBS came along later.) It’s unlikely Oldsmobile would have tried to adsvertise on the radio until there was a nationwide network for it to advertise on.