On the proper use of `tl_rescan`

Looking at the code below, what would the setup in 6. have to be to return F? Also, why does 2. return F in other words how are group_begin: and c_group_begin_token different?

begin{enumerate}
item tl_if_head_is_N_type:nTF{{foo}}{T}{F} % 1. F
item tl_if_head_eq_catcode:nNTF{{foo}}group_begin:{T}{F} % 2. F
item tl_if_head_eq_catcode:nNTF{{foo}}c_group_begin_token{T}{F} % 3. T
item token_if_group_begin:NTFc_group_begin_token{T}{F} % 4. T
item tl_if_head_is_N_type:nTF{[foo]}{T}{F} % 5. T
item tl_if_head_is_N_type:nTF % 6. T
{tl_rescan:nn
  {char_set_catcode_group_begin:N [
      char_set_catcode_group_end:N ]}
  {[foo]}}{T}{F}
end{enumerate}

UPDATE:

What was lost on me the first time around is that using predicates such as tl_if_head_eq_catcode:nNTF as second argument totl_rescan is a bad idea to detect any change to catcode specified in the setup as they are affected by the change themselves. That said, perhaps this new MWE explains better what I was trying to lead to.
Also, [I’m now clear ongroup_begin: vs c_group_begin_token].

char91 % [
char93 % ]

cctab_const:Nn c__erw_setup_cctab
{
  cctab_select:N c_code_cctab
  char_set_catcode:nn  {91}{1}
  char_set_catcode:nn  {93}{2}
}

tl_rescan:nn{c__erw_setup_cctab}
{tl_if_head_eq_catcode:nNTF {{foo}}
c_group_begin_token{T}{F}} % T

exp_args:Nnx
tl_rescan:nn{c__erw_setup_cctab}
{tl_if_head_eq_catcode:nNTF {[foo]}
c_group_begin_token{T}{F}} % F

PS: feel free to delete the question if it’s still not clear.