EX = 2:
Black's group has eight effective liberties, and a larger eye. White's group has two false eyes.

:
Black takes a liberty of White's lower chain, to attack her false eyes.

:
White's best policy is filling in her false eyes. But Black occupies the -points.

:
For the sake of simplicity, we will stop the sequence here, and not re-capture the ko. The number of Black's ko-threats needed to win is t = ( + ) - 1 = 3 only. The -points cannot be counted for White any more.

EX = 2 / -f:
We exchange a false White eye against an outside -liberty.

:
White's best policy is capturing the ko "early".

:
White fills in her false eye as a ko-threat. We stop the sequence here.

The number of Black's ko-threats needed to win - from here on - is t = ( + ) - 1 = 3. In total, Black needed four ko-threats to win. The original -point counts for White again.

Filling in her first false eye has proven advantageous for White.

EX = 2 / -c -f:
Additionally, we exchange a shared -liberty against a Black -liberty and two White -liberties.

Please note that - in "real life" - this exchange would be equivalent to Black losing a move.

:
White's best policy is filling in her false eye. But Black occupies the -point.

The number of Black's ko-threats needed to win is t = ( + ) - 1 = 4. This is the same as before the exchange.

However, White's group has six liberties left, so there will be no ko. In the problem, White will choose the semeai against Black's lower right corner, so winning the game unconditionally.

So Black should have given priority to occupying outside liberties.

EX = 2 / -c -2f:
Finally, we exchange the second false White eye against another outside -liberty.

t = ( + ) - 1 = 4. This is the same as before the exchange.

EX = 2 / -2f:
As we know already, filling in the second false eye - in exchange against the remaining -liberty - is not correct for White.

t = - 1 = 3; so White lost a move (and simultaneously the Punishment Semeai), as well as a Black ko-threat.

EX = 2 / -c:
Starting from the basic position, we exchanged a shared -liberty against a Black -liberty and two White -liberties. N.B.: Please assume all -labels in the diagram to be valid liberties.

:
White's best policy is filling in her false eyes. But Black occupies the -points.

The number of Black's ko-threats needed to win is t = ( + ) - 1 = 4. This is one more than before the exchange.

Again, we got a clear sign that Black should think twice before occupying shared liberties too early (i.e. as long as at least two outside liberties are available).

Conclusion:

Filling in her first false eye is advantageous for White. At least, this move will not do any harm.

However, additionally filling in her second false eye may be a White mistake, if this move is played unforced (i.e. there are two many shared liberties of her lower chain left).

Black should refrain from occupying shared liberties, as long as these moves do not force White to fill in her false eyes (and cannot also be used as ko-threats), and as long as there are at least two White outside liberties left.