I'm just now running into this issue of tab order not being available:
OS X 10.13.3
Safari appears to simply not tab anywhere new - it leaves the current field (i.e. no flashing cursor) but it doesn't show up anywhere else. I have cleared the entire tab order for the layout except for the 3 fields I'm interested in. This is a Custom Theme - but I don't know what Theme was used when this layout was first created.
These fields are in a slide control, if that matters. Oh wait - it DOES matter! If I put these fields out in the main body and not in the slide control, the tab order works correctly. I'll do some more investigating - perhaps rebuilding the slide control from scratch will help.
No, creating a new slide panel doesn't help.
Nope, creating a whole new layout (using the same custom theme) didn't help.
Changing the theme (on the brand new layout) to Classic Refined Warm didn't help.
It seems to be a slide control issue...Ah! But...tab order on the FRONT slide panel DOES work as expected. And maybe on Panel 2 (of 3) also seems to work. But the tab order on the 3rd panel still doesn't work.
Field 1 (of 3) is a regular edit box; fields 2 and 3 are concealed edit boxes.
Hmm...I guess I can get the tab order on the Front panel to get messed up, too. It's almost like the browser is applying it's own order based on the location of the object: if I put the fields left to right above a 4th field, then it goes left to right, then #4, then back to #1. But if I move the same 3 fields so they are vertically stacked, and space them out so that field #4 is positioned somewhere in between (e.g. the visible order is something like 1, 2, 4, 3), then the tab order goes 1, 2, 4, 3 (instead of the 1, 2, 3, 4 that I defined).
In either case, on Panel #3, regardless of field type and visible order on the page, it doesn't cycle at all. If I start in #1, it doesn't go to 2 or 3. Starting in 2 doesn't go anywhere, etc.