There are some preliminaries to answering your question.
First, the concept of a cadence is most well-defined with respect to music of the Common Practice Era, which is shorthand for "mostly European art music composed from about 1650 to 1900". We can (and do) extend the concept of "cadence" outside of that narrow category of music, and when we extend, we have to relax the "rules" in different ways, or else we can't effectively apply the concepts of cadences in other contexts. So I suggest being a bit relaxed in any analysis of cadences in music such as jazz.
Second, the core aspect of a cadence that can most effectively be extended outside of common practice music is the idea that a cadence is a point of repose. In other words, if the music feels like it's making a kind of pause, like a comma or period in grammar, then we can think of that as a cadence. Without this aspect of the notion of cadence, any time we had a V chord followed by a I chord would be a cadence and that would destroy the meaning and usefulness of the concept itself.
Before commenting on deceptive cadences, I'm going to first assess where there seem to be cadences in the music in question.
Based on the above recording, I don't agree that there's a cadence at all on the vi chord in measure 9 of "At The Jazz Band Ball". I hear a (brief) point of repose in measure 8, which would make that a half cadence (F is the V chord). Measure 9 is the start of the next phrase group.
Regarding the second cadence you're asking about, I think it's measures 25-29 where we see VI7 - VI7 - II7 - II7 - IV - iv(5b) that you're asking about. Since there's no repose in any of those measures, there's no cadence of any kind. Measures 26 and 28 have half notes that could feel like pauses, but to my ear they are repeats of a rhythmic motive that is still moving the music forward. In any case when we hear the IV chord in measure 29, the melody is still quite active. The next cadence I hear is at measure 32 which we could call an "authentic cadence" or just see it as a quintessential jazz turnaround of VI/vi - II/ii - V - I.
For "Sunny Side of the Street", the first point of repose I hear is again in measure 8 (this is common in big band jazz). And of course measure 8 is another ii - V - I cadence. Measure 16 in this is an interesting example of where I hear a cadence despite there being continued motion in the melody and less repose. In a way I think we're prepared to hear that as a cadence because it is a repeat of the first cadence in measure 8, and also because it closes out the second 8 and we are expecting an aaba form.
This type of jazz can have deceptive cadences, but I feel like they are less often written out in the chart and more likely appear at the end of the final statement of the head where the band will add 4 - 16 bars to draw out the finish. In answer to your question, when we hear a point of repose that is not clearly on tonic or dominant harmony, and especially where the piece continues to a later cadence to the tonic, we can reasonably describe that as a deceptive cadence.
I hope one takeaway you get from this answer is that many times, we cannot effectively read cadences. We have to listen to hear (and feel) cadences.