Wanting to prototype something with an oddball push-pull 3.3V-to-13V switch led me to concoct an experiment using only stuff available at a reasonably well-stocked Radio Shack, with particular attention to ICs that provide push-pull outputs. So far I’ve tried configurations based on the original 555 timer and the TL082 op amp.
My first experiments with the TL082 in Schmitt trigger configuration were not promising, but I’m suspicious something may have been connected wrong; the logic low never went below 1.15V, which happens to have been the reference voltage, half of 3.3V. Either way, the supply voltage had to read 17.3V for a high output of 13V.
In contrast, the 555-based Schmitt trigger appears to be a workable solution, as long as you can drive the chip 1.5V higher than the desired high output.