0800 890 595 is now a (quite rare) example of the equipment engaged tone.
I haven't done much looking for interesting switching/signalling since the early 2000s. It's got more difficult now because most people and businesses in poor countries have jumped straight to GSM (+successors).
Back then, it would (as radio_phreak notes) be much more productive to look in the provincial towns and cities of poor countries than in their main cities.
My preferred method was to look online for hotels or businesses in those backwater areas, ideally finding their fax numbers, and call those. Much prefer bothering a fax machine than disturbing a person.
Now-a-days you need to do this armed with the country's dialling plan (wikipedia usually has these) - and most of the numbers you find will be mobiles.
Re Cuba, I can't reach the supposed second dialtone for the US base via +53 99.
The state telco is marketing the "fija alternativa" service - ie a GSM-based fixed service - suggesting aged and interesting POTS equipment exists.
Calling from here, it's evident that their international gateway is something not outrageously ancient, because it promptly returns an appropriate SS7 code for incorrect prefixes -
eg +53 41 000000 returns the usual SIT+"the number you have dialled has not been recognised" from my local exchange.
+53 xx 300000 returns a Cuban intercept - in Spanish then English - after about 5 seconds of delay, where XX is any of the 2-digit areacodes listed at https://en.wikipedia.org/wiki/Telephone_numbers_in_Cuba. Sadly no signalling sounds are evident during the delays - I think I've tried all of them.
I had a quick look for hotels in Panama and all the phone numbers I found were +507 6xxx xxxxx - ie mobiles.
However, again, I'm hopeful that downstream of the international gateway is something elderly and interesting.
+507 900 0000 sometimes gives an intercept - Spanish only - mentioning C&W Panama, again with a significant post-dial delay.
+507 800 0000 gives my local telco's equipment engaged tone.
+507 811 1111 was answered by a human
+507 700 0000 is a different Spanish intercept, with a longer post-dial delay.
+507 600 0000 or 500 0000 give my local telco's SIT+number not recognised intercept.
+507 400 0000 is the same intercept-after-delay as 900 0000.
+507 300 0000 is yet another Spanish intercept, with delay.
+507 200 0000 has a very long delay then something times out any my local telco plays SIT+"sorry, there is a fault".
+507 210 0000 has a long delay then the 900 0000 intercept
+507 220 0000 rings, again after a delay, and is answered by some sort of automated service - in Spanish.
No signalling sounds or evident, for me, in any of the above :-(