i highly highly doubt that the light is causing problems.
this is my 6 gallon, with 30 watts of PC light (2x volume, 2x light wattage) -
its also important to remember that corals that are deprived of adequate levels of light do NOT close up, as wea's zoos have. instead, they undergo morphological changes such as stalk extension and oral disk expansion, as well as increased zooxanthellae production in an effort to bolster more photon energy.
one also must remember that wattage per gallon is not a very accurate measure of total light energy being transmitted onto the coral surface, taking into the account of the inverse square law regarding decreasing light intensity over distance.
thus, the 120 watts of light over a 20 gallon may actually yield less usable light than 18 watts over 3 gallons, because of the increased distance that the light has from the coral! As an aside, imo 120 watts IS rather low light for a standard 20 gallon, given it's height.
i would suspect water conditions being the culprit here - remember, in nano and pico tanks, if one thing dies and causes an ammonia spike, it can easily cause a huge chain reaction of dying organisms, and subsequently released toxins. we all know that many stressed corals, especially zoanthids/palythoa/protopalys, have the ability to create extradinarily dangerous chemicals even to other corals in the tiny confines of our aquaria.
what type of tests are you using to test water conditions? check the expiration dates. especially calc and alk tests - these two parameters being off could easily yield the symptoms you have described.
possible scenario - adding too much iodine or calc/alk supplements last week may have caused a stresed or unhealthy coral individual to succumb releasing a cloud of toxins/organic chemicals that cascaded into a tank crash.
stray voltage in the tank may also cause symptoms described, as would the introduction of heavy metals such as copper. anyone drop a coin into your tank by accident? air freshener around? smoking cigarettes? all these types of aerosols can become bound in salt water and cause damage to your corals.
use a polyfilter in your filter and see what color it changes.
just a few ideas...