During fumigation of the room
While fumigating the room.
We don't say "during fumigating the room" because during wants a noun or noun-phrase complement whose action or existence occurs over time.
during the game
during interrogation of the suspect
And even though -ing forms can function as nominals, when you include a direct object and emphasize the time-aspect, as during does, it makes them act like verbs, and we use while with continuous verbs.
But what about a single word like sleeping? There's no direct object there. Can we say "during sleeping"? No, we say "while sleeping" or "during sleep". If you emphasize the time-aspect, the word acts like a verb. So maybe all that is needed to turn the -ing form into a verb is to emphasize the time-aspect. At least when the verb is intransitive.
You could counteract this emphasis with transitives by using an article or adjective, as that pulls the word back into noun territory:
During the fumigating, wear a mask.
During extended fumigating, wear a diving suit.
Though those might sound a tad off to a some percentage of speakers when there is a frequently used abstract noun available as is the case with fumigation.
You can also "convert" or "cast" the -ing form to a noun with an attribute, either before the word or as a complement that attaches the attribute back to the head noun:
During tank cleaning, wear goggles.
During cleaning of the tank, wear goggles.