Oh yeah, the old Rainbow sauna in Taipei. Brings back good memories. I went there a few times during my first visit to Taiwan in 2011. The facilities were kinda basic and a bit old, but there were lots of young twinks among the crowd. I was in my early 20s so didn't have any problems getting in or finding action once there. I remember people were actually very friendly as I was a bit shy. I was pretty much still a newbie when it came to gay saunas at that time. I had just been to two of them the year before in Seoul. You're absolutely right that the location of Soi 13 in is not that of Rainbow. I was told that the building of Soi 13 in used to be a karaoke bar before, and that explains the layout of the cabins and the cruising area in the lower floor.
Also remember that Aniki sauna was all the rage 10 years ago, as the facilities were all brand new and the crowd tended to be younger and more muscular, albeit it was much pricier than Rainbow. I went a few times and it was truly a lot of fun. I think the last time was in 2016. Taiwanese friends told me that in the last few years it had become just a shell of its past self. The facilities were deteriorating fast, the crowd became much smaller but it still continued to have a higher entrance fee that Soi 13in. Read that it closed at the end of 2020. I guess, it means that the crowds at Soi 13 in will be even bigger now.
I agree with @PeterRS about the friendliness of Taiwanese guy. Way more than Singaporeans or Hong-kongese imo. Good advice about Commander D (or just CD as local boys call it). I would also recommend another bar called the Hunt, especially on their towel night. You pretty much are given a towel when you get in and that's how you go around the bar. They have a dark room, which gets really steamy:). I was surprised to see it referenced in a gay Taiwanese movie called "The Story the Stone" (a modern gay retelling of one of the greatest classics of Chinese literature).
For apps, beside Grindr and Blued, I would also suggest Hornet. It's quite popular in Taiwan and in a few other Asian countries.