OK - in a real bad mood with the cab

[grinder]

honestly no

and i can confirm that the reverse lights DO come on when you select reverse .. not looking good is it !

[bumpstart]

/\\ depends,,, depending on the car and model of 3N/4N 71B,, some have the selection position switch on the T bar,, and others have them at the box
 
( i have a box and T bar here from different cars and both have a switch ! )
BTW s4 are all bar linkage
,,,, if you have a cable with cable select brake you have an s5 auto and it is not a jatco 4N71b

the effect of a fault on types with a T bar switch
is that the T bar and dash ( and rev lights ) may indicate the correct position
,, but that is not necessarily so at the lever directly on the box

it is easy to take out the split pin and drop the linkage to test it

be sure the rear wheels are in the air while you test in case it does select a gear while your under it