Ok Bigtone53 as you were probably the nearest anyway. Here is the answer in all its gory detail.
It sounds like I swapped two digits in this sequence. Who am I and why?
The person I was looking for was songwriter Bobby Troup, who wrote Route 66.
Square root of 66 as a continued fraction (yes those again)
Labelling the locations mentioned in the song Route 66 in geographical order (Starting in Chicago ending in LA).
8 Chicago Illinois
8 St. Louis, Missouri;
16 Joplin, Missouri;
8 Oklahoma City, Oklahoma;
16 Amarillo, Texas;
8 Gallup, New Mexico;
16 Winona, Arizona;
8 Flagstaff, Arizona;
16 Kingman, Arizona;
8 Barstow, California;
16 San Bernardino, California.
8 Los Angeles California
Bobby Troup reversed the order of Winona and Flagstaff in the lines "Flagstaff Arizona, don't forget Winona" to get a better rhyme. => 8,8,16,8,16,8,8,16,16,8,16,8
Along the way we had extra hints
Follow the sun = Travel west. Beckham went to LA Galaxy, obviously for 'kicks'.
"Bend it like Beckham" actress Parminder Nagra plays Neela Rasgotra in ER (A Chicago hospital filmed in LA). (They've gone west even though they pretend they haven't).
“A Young Man is Gone” Lyrics by Mike Love, based on the melody of "Their Hearts were full of Spring" by Bobby Troup (this wasn't much help)
Thought I'd chuck that in. (allusion to Chuck Berry)
Sir Alf's finest moment on Wembley Way. (His route in 66).
She was out of order on December 12th 2001. (Winona Ryder arrested for shoplifting in Beverly Hills).
Finally harking back to the biscuit teaser Abraham Lincoln was married in Springfield, Illinois which is also on Route66.