I don't think of each separate "tonicization" in a chain of secondary dominants--in such cases, I just think "secondary dominants" or whatever my internal shorthand for that is. However, I do think of temporary tonics when I see V-I, ii-V (or iiø-V), ii-V-I or vi-ii-V subsequences (in keys other than the main one) embedded within such fifth progession chains. Temporary tonicizations are implied by the chord types used in fifths chains--and vice versa. So by thinking of the temporary tonics, I can more easily memorize and recall the appropriate chord types, as well as follow these sequences easily on the fretboard.

Come to that, stray chords (like the Bb7 in the first post) often turn out to be tritone substitutions in fifth progressions. In the first post, the Bb7 chord can be seen as a tritone substitution of some kind of III chord (Em, E7, Em7...), so from B on we essentially have a 7-3-6-2-5-1 fifth progression, mostly of secondary dominants. D7 could also be replaced by a tritone substitution (like Ab7 or Ab7b5), adding a little color and continuing the initial chromatic root descent even farther. You might even try Ab9, Ab9b5 or Ab9#5, particularly if you follow with G9 rather than plain G7.

To take the chain a couple of steps farther: in the sheet music, the chords in the first few bars of the chorus (as extracted from the piano part) run like this:
1 4 | 1_b77- 6[7]_6ø | 27 59_57+ | 1[6] |
Note the 4 in the first measure. Now, in fifth progressions involving the 4th, it's common to short-circuit the path around the circle (and avoid a slew of non-diatonic roots) by moving the 4 root by a tritone rather than fifth, thus to 7 rather than to b7. If for the second 1 we substitute 7 (the B chord which occurs in the corresponding position in the first post), we end up with a complete short-circuited fifths circle. In simplified form this is:
1 4 | 7_3 6 | 2 5 | 1
Pretty nifty, eh?