Agnosticism may not itself be a philosophy, but a relevant and respectable agnosticism will proceed from two philosophical principles: one epistemological and one ethical. What this means is that a person's agnosticism should be based upon their philosophy and knowledge and their moral philosophy. When this happens, it means that their agnosticism is not just philosophical, but well-considered and reasonable.
Agnosticism & Epistemology
Epistemology is the philosophy of knowledge and belief. Thus a person's epistemology describes what they think can be known, how knowledge can be acquired, and what the basis for reasonable beliefs should be. Since agnosticism is the position that one doesn't know if any gods exist or not, than a reasonable conclusion that one does not know if any gods exist will be derive from what they think about knowledge generally and how knowledge generally can be acquired.
As Robert Flint explained in his 1903 book Agnosticism, agnosticism is:
...properly a theory about knowledge, not about religion. A theist and a Christian may be an agnostic; an atheist may not be an agnostic. An atheist may deny that there is God, and in this case his atheism is dogmatic and not agnostic.
Or he may refuse to acknowledge that there is a God simply on the ground that he perceives no evidence for his existence and finds the arguments which have been advanced in proof of it invalid. In this case his atheism is critical, not agnostic. The atheist may be, and not infrequently is, an agnostic.
So if a person is a weak agnostic and simply says that they personally don't know if any gods exist, then their agnosticism is reasonable or not depending on whether they really do lack the grounds for claiming knowledge. Their epistemology will be the basis for whether they think they have such ground.
If a person is a strong agnostic and says that no one can know if any gods exist or not, then their agnosticism is reasonable or not depending on whether they have sound, valid arguments for the absence of any possible grounds for claiming such knowledge. That argument will depend largely on the soundness of their philosophy of knowledge, i.e. their epistemology.
Agnosticism & Ethics
The second philosophical principle mentioned above is ethical and it will come into play when a person argues to whatever extent that we have an ethical duty not to assert knowledge claims for ideas which we cannot adequately support either through evidence and logic. Such a position is likely to be held whether one is weak or a strong agnostic, but it's more likely to be held implicitly with weak agnosticism and made explicitly with strong agnosticism.
With weak agnosticism, a person is simply describing their own state of knowledge and aren't making any claims about others generally. They have already determined that they lack sufficient grounds to make a knowledge claim, but so what? Why not claim knowledge anyway? The answer to that is ethical in nature, thus refusing to claim to know if any gods exist involves ethics as much as epistemology. But since it's a personal position being adopted, the ethical part is unlikely to be argued explicitly.
Ethics is involved in the same way with strong agnosticism, but the ethical component is more likely to be argued explicitly because the person is also making an argument for what others can or cannot know. They need to make an argument for others adopting the same epistemological theory that they have as well as the same ethical standard, at least when it comes to situations like these.
This ethical standard about not making knowledge claims without sufficient grounds can be traced to William K. Clifford, an English mathematician and philosopher who did not end up writing much, but nevertheless became famous for his argument that beliefs are not simply private acts. They are, instead, public acts and therefore have moral consequences. In his essay "The Ethics of Belief" (1879), he expressed the controversial idea that: "It is wrong always, everywhere, and for anyone, to believe anything on insufficient evidence."