As the F5 LTM does not come with an NTP health monitor, I began my search for one. I found one here, written for 9.x and spent a few minutes getting it to work in 11.5.4.
Disclaimer: All the hard work was already done, I simply made a few updates to it for 11.x:
External Program: ntp_mon
Works on v12.1 as well.
hmm..does not seem to be working on 11.5.3
Seems to work properly on 12.1.2 also.