Tbh I don't see Goku (vs Tambourine) as different from Goku (vs Tenshinhan)... Goku ate that fish, punched the rock and said "that's nice!" or something like this... There was no hint of a power increase there. We don't know if Goku were receiving power boost from near death experiences — Kuririn said that in the Freeza saga, but Kuririn wasn't around at anytime when Goku got those big boosts... Yeah, he noticed Goku was even stronger than in the 21st Budokai when Goku was fighting General Blue, but Goku had also been in many battles until that point... Which to me counts as a way of training. The very significant boosts came from training with Karin, then when drinking the mysterious water, etc... Kuririn was only around, when Goku got stronger, when both of them trained together. Kuririn may have been rationalizing the instances Goku got a boost that he had no explanation for. I think that, unless noticed, Goku's strength didn't change. Goku could have said upon recovering his strength that he feels even stronger, but he did not.
So since Goku vs Tambourine was pretty one sided, while Goku vs Tenshinhan was a close battle, with Goku having a slight superiority, to me Tenshinhan defeated Tambourine with no problems. He'd likely have a harder time than Goku, but it wouldn't be too difficult, though. Let's say he'd need to be serious and using full power to defeat Tambourine, maybe Tambourine could land a shot or two, but he'd more than likely defeat Tambourine without needing anything extreme like the Kikoho imo.
