Installing a generator transfer switch on an ITE Pushmatic panel
Interesting panel.  Ours is very similar but with a BR-style 4-throw 200A breaker above the two 7-row buses.  Ours went in in the 1980s, but prior to that the cost of those huge 200A breakers was prohibitive.
It appears your panel has the same 7-row buses, but it simply uses a larger value (e.g. 60A) Pushmatic breaker in the top position, back-fed... giving 1 main breaker per bus.
Having 2 main breakers was legal under the old &quot;Rule of Six&quot;.
In point of fact, it's still legal under the rules for 320/400A service; those are simply connected to dual 200A main panels.  Think of yours as &quot;That, inside one chassis&quot; (which is also done on many 400A meter-mains).
Doing this as you intend is straightforward.
Much as I loathe those 6-8-10 circuit transfer switches, my top reason is the absurd price.  $350-450-550 for something that simple is just insane, especially given how limited they are.  But I have to admit when you're dealing with an &quot;obsolete&quot; panel like this, that's kinda the use-case for these things.
If only...
That said, I really wish I could get a closer look at this panel's innards. Both for academic curiosity, and because I suspect the internal arrangement is ... highly exploitable.  I think an external transfer switch could be wired to throw over one of the two internal buses to generator, giving you 12++ loadable circuits instead of 6.  It would be contingent on AHJ approval, but it seems doable.
The way I'd do it would be to have a second main panel right next to it, of modern stock, probably a Siemens 30-space main-lug with their $25 ECSBPK01 interlock in it.  I would double-feed the panel off the meter (exactly as done with 400A service).

Routine stuff, the &quot;Utility&quot; breaker has the same breaker size as the existing Pushmatic main breaker for that bus; the &quot;Gen&quot; breaker is whatever the generator needs. These breakers are back-fed.
Then, I'd come off the main lugs of this panel (which are on the breakered side since we're backfeeding) and go over and feed the top of the Pushmatic breaker in the bus we are switching over.   At this point, that half of the Pushmatic panel is switchable, as are all the remaining spaces in the Siemens panel for future circuits, modernization, etc.
The main snag I see is that the neutrals for the circuits on the generator-switched side need to be on their own neutral bar fed off the Siemens panel... but I bet Pushmatic gave you two neutral bars.
As time and leisure permits, you could move circuits over to the normal Siemens breaker spaces, and retire the Pushmatic panel for good, or simply leave it in place as a large junction box.
You could do AFCI/GFCI breakers in the Siemens panel.

Or make the Pushmatic the subpanel
Another plan would be to install the new panel as the one main panel (think $120 for the panel + $70 for a gen interlock for that panel)... and then, feed the Pushmatic panel as a subpanel of this panel.  That would place every breaker space in the entire house under the generator interlock, meaning absolutely no branch circuit rewiring is necessary; just the service wires from meter to new-main, and the feeder wires from new-main to Pushmatic.
In fact, this could be an outside panel, which would satisfy NEC 2020 requirements for outside interlocks... or even a meter-main, which would require almost no wires run at all.
Well, you'd have to run the cable to the generator inlet in any case.