Symbolism, Imagery, Allegory
Pens, as you can probably figure out from the spelling, are a common substitution for penises. Tristram spends a lot of time thinking about and describing his pen (typical guy). He acts almost like his pen has its own personality—it gets tired, and has moods: "in one mood giving rash jerks and hair-brain'd squirts" and in another "spurting [his] ink about [his] table and [his] books" (2.21.2). It gets "fatigued" describing his European journey (7.43.7), and affected by Tristram's ill health, when "the thoughts rise heavy and pass gummous through [his] pen" (9.13.1).
Basically, the pen is an extension of Tristram's body. Okay, so maybe it's not his penis (sometimes a cigar is just a cigar—but, let's be honest, usually it's not)—but that's a lot of love for your standard-issue BIC. He transfers his own feelings onto it, blames it for being tired when he's the tuckered one and accuses it of going astray when his thoughts are running wild.
Without a nose or a complete penis, Tristram turns to the pen as a symbol of his masculinity, and his masculinity is a symbol of his ability to write—or maybe, his writing is a symbol of his masculinity. This scribbling masculinity is different from the kind that Mr. Shandy appreciates. Remember, he approves of his stud bull because the bull goes about his business—mounting cows—with absolute seriousness. But Tristram can't do anything seriously.