Indirect Function: Use Cell For Sheet Name

Cell F4 contains a worksheet name which was “calculated” by an IF function (IF something, then ‘T2’, otherwise ‘T3’).

Cell F5 must then look at either sheet T2 or sheet T3 (depending on what it is told to do by reference to cell F4 just above) and report what it finds in cell A1 there.

Clearly I must use the INDIRECT function. But I have tried every imaginable combination of single and double quotation marks to produce the equivalent of
=T2!A1
all to no avail.

Is it something to do with letter and number combinations?

Alternatively, how else should I achieve what I want?

PS F4 could have been “calculated” by any other means, e.g. =MONTH(TODAY()).