Jon Astley (no relation to Rick) began his career as a producer, and was particularly well-known for his work with The Who (he was, for a time, Pete Townshend's brother-in-law). Later, Astley built a second career as an expert in re-mastering material for the conversion to CDs.
In between these pursuits, Astley also released two solo albums and managed to have two charting singles (the other one was 1988's "Put This Love to the Test" and no, I don't remember it either). "Jane's Getting Serious" is a catchy pop song, with a choppy percussion-driven sound. The song peaked at #77, while the album Everyone Loves the Pilot (Except the Crew) reached #135.
By the by, "Jane" was also used in a series of Heinz Ketchup Commercials, including one featuring an early role for future Friend Matt LeBlanc, so you may have heard the song there.
The video seems to take place on a deserted island and is highlighted by three dancing gorillas. Perhaps the chaps from Haircut 100 are singing on the same island, who knows? At any rate, it is a solid video of a mostly forgotten pop gem.