While working with Marcello on AI this summer, I've noticed that I have some standard mantras that I invoke in my inner dialogue (though only on appropriate occasions, not as a literal repeated mantra). This says something about which tropes are most often useful - in my own working life, anyway!

"If anyone could actually update on the evidence, they would have a power far beyond that of Nobel Prize winners."
(When encountering a need to discard some idea to which I was attached, or admit loss of a sunk cost on an avenue that doesn't seem to be working out.)
"The universe is already like [X], or not; if it is then I can only minimize the embarrassment by admitting it and adapting as fast as possible."
(If the first mantra doesn't work; then I actually visualize the universe already being a certain way, so that I can see the penalty for being a universe that works a certain way and yet believing otherwise.)
"First understand the problem, then solve it."
(If getting too caught up in proposing solutions, or discouraged when solutions don't work out - the immediate task at hand is just to understand the problem, and one may ask whether progress has been made on this. From full understanding a solution usually follows quickly.)
"Load the problem."
(Try to get your mind involved and processing the various aspects of it.)
"Five minutes is enough time to have an insight."
(If my mind seems to be going empty.)
"Ask only one thing of your mind and it may give it to you."
(Focusing during work, or trying to load the problem into memory before going to sleep each night, in hopes of putting the subconscious to work on it.)
"Run right up the mountain!"
(My general visualization of the FAI problem; a huge, blank, impossibly high wall, which I have to run up as quickly as possible. Used to accomodate the sense of the problem being much larger than whatever it is I'm working on right now.)
"When the problem is solved, that thought will be a wasted motion in retrospect."
(I first enunciated this as an explicit general principle when explaining to Marcello why e.g. one doesn't worry about people who have failed to solve a problem previously. When you actually solve the problem, those thoughts will predictably not have contributed anything in retrospect. So if your goal is to solve the problem, you should focus on the object-level problem, instead of worrying about whether you have sufficient status to solve it. The same rule applies to many other habitual worries, or reasoning effort expended to reassure against them, that would predictably appear as wasted motion in retrospect, after actually solving the problem.)
"There's always just enough time when you do something right, no more, no less."
(A quote from C. J. Cherryh's Paladin, used when feeling rushed. I don't think it's true literally or otherwise, but it seems to convey an important wordless sentiment.
"See the truth, not what you expect or hope."
(When expecting the answer to go a particular way, or hoping for the answer to go a particular way, is exerting detectable pressure on an ongoing inquiry.)

I don't listen to music while working, because of studies showing that, e.g., programmers listening to music are equally competent at implementing a given algorithm, but much less likely to notice that the algorithm's output is always equal to its input. However, I sometimes think of the theme Emiya #0 when feeling fatigued or trying to make a special demand on my mind.