Pituitary gland makes testosterona.
Nope. The pituitary makes Follicle Stimulating Hormone, and Luteinizing Hormone, to make sperm/testosterone, respectively. But FSH and LH stimulate the cells (such as leydig cells) in the testes to make these things. No nuts, no sperm/test from the nuts. And the pituitary is activated by factors released from the hypothalamus, which detects changes in blood concentrations of sex hormones.
So, in a eunuch, there's the likely possibility that your LH and FSH levels would be off-the-chart high, as your body tries to fix the fact that the hypothalamus can't detect testosterone. Eventually, it would all even out thru negative feedback loops...the pituitary and hypothalamus, though wanting to produce test, would be over-whelmed by the excessive negative feedback loops caused by high levels of FSH and LH (however ineffective they may now be).
That said, it is possible to produce testosterone in the adrenals. Women have testosterone in their bodies, and the adrenals are the source. Not all the testosterone made is aromatized in the body to estrogen quickly enough, leading some women to have a higher than average sex drive, or more classically defined "male" secondary sex characteristics, such as lowered voices, broader shoulders, a more hirsute appearance, or clitoral growth. Pretty much, the average female bodybuilder.
The adrenals making test is not enough to virilize a man into a man. Although, mutations that lead to virilization in women show dysfunctional adrenals that over produce testosterone. The rather small increase in women is enough to virilize them. But over-active adrenals can't turn an un-virilized boy into a man.
You'd need testosterone replacement therapy, plain and simple.