Secret hot spring path is back of the gambler in South stronghold , if I remember correctly you have to talk to several NPCs throughout Central,the snow country (forgot the name) & ebron to trigger or else you can't get there .
In Ebron - the elf wandering near Treehouse,
In Red Keep - The solider on roof of right side of building by climbing the ladder,
In Thremten - A guy in the house where healer (cleric) stands in front of the door.
In Capital - Two women having a conversation in the Inn.
Paverhill - Woman standing in front of fireplace inside building near left entrance.
There is one more person , A Elf who is searching for the secret hot spring just like you somewhere in begus.
That's all I can remember , Check on the end of the path on left side of gambler in Calbridge Stronghold if you found most of the NPCs.
The elf who is searching for the secret onsen is not in Begus, she is in Witton. ;-)
Also, what you have to know is that you have to interact with the border of the screen on the path in order to trigger the access to the next screen, I had a hard time to find the secret onsen because I tried to follow the path to the next screen but didn't interact with the border of the screen at first so I thought I was wrong and searched elsewhere when I was right, it was there. :-3