u/Myrmidon99 has a great answer here about kamikazes in general here:
From this it seems like this wouldn't really make any sense. The nature of increasingly inexperienced conscripts coupled with the complexities of aircraft, weather, and navigation, meant at least a quarter of aircraft returned to the base safely after mechanical issues, inclement weather, or simply failing to find the targets (edit: or as the question is addressing, they may have had "engine trouble," as opposed to engine trouble, but that would only work so many times, but the fact that it worked at all is a sign that returning to base was understood to be sometimes necessary).
They were not expected to waste their airplanes or lives flying around aimlessly. A number of kamikaze myths focus on the intended one-way nature of the trip, for example not giving them enough fuel to return and land, or training them to land. That's just too impractical for ww2-era aviation (and also makes the airplane a less effective weapon).
Did this really happen?
I know that I've never come across anything even suggesting that the described "motivational item" was ever used on pilots heading out to fly a kamikaze mission. That doesn't mean it didn't happen... it's not like there's going to be a document somewhere that'll state "We, the commanders of the Kamikaze units of Japan, vow to never use the following methods of motivation...".
My guess is that it's just another internet fable, just like saying that the planes only had enough fuel for a one-way mission or the pilots weren't taught how to land.
Source: it's awfully hard to prove a negative.