When Bulma suggested killing Gero, Tenshinhan said that he wanted to test his strength against them, and dying wouldn't bother him (Not really the exact words, but same general meaning). That's the last time he talks about his reasons for training. If his reason truly is "to test his strength", his motivation is unrelated to Goku, and he wouldn't stop training after the Cell Saga.It's true Ten was still in high hopes of being able to catch up, and possibly surpass Goku with harder training from Kaio-sama, and with a few "tweaks" of his own, but as stated by Tenshinhan later, "Then...this "Super Saiya-jin" that Goku's become... ...is the most powerful being in the universe... ...it's as if he's in a completely different world now..." He recognized how far Goku surpassed him now.
Besides, unlike Kuririn and Yamcha, who were shown to lead normal lives and wear common clothes, Tenshinhan still was a mountain nomad and is even show wearing clothes extremely similar to the weighted training clothes that Kamisama gave him in the Saiyan Saga (only the shirt was sleeveless) while dodging Buu's blasts. There's no proof at all that his life style changed after the Cell Saga.
Bad Example. Kuririn wanted a girlfriend, and he stopped practicing after he got one...Kuririn was also a martial artist with reasons of his own when he arrived on Muten Roshi's island and requested training, but he stopped eventually.