I hope my advice is helpful to you.
As you know, one word(Korean) is used with lots of meaning.
‘면’ = if
‘볼테면’ = if you wanna try(the speakers’ willness is include)
But we don’t use it only ‘볼테면’, it need to plus other Verb.
Ex. ‘해볼테면’ = if you wanna try to do, (cf. do=하다)
‘맛볼테면’ = if you wanna try to taste, (cf. taste=맛보다)
But, ‘볼 테면’ = if you wanna try to see, (cf.보다)
‘볼 테지’, without other words(Subject/object), I am not sure what you mean.
Ex, 볼 테면, 볼 테지 = if you wanna try to see, just see it!
But this sentence’s nuance is like to complain or grumble.
If you wanna see it, just see it without any saying, huh!
When = 하면, 할 때(up to the situation)
When you finish your homework, you can go out.
네가 숙제를 다하면(다 할 때) / 끝내면(끝낼 때), 너는 나갈 수 있어.