Any comment about God's divine nature is pure speculation - we are not told!!
What we do know is that the many statements about God's emotions are anthropomorphisms - an attempt to convey impossible -to-describe-information by making it like what we are used to - human. But God is not human so exactly what goes on with Him we do not know.
We are definitely told that God is invisible (Col 1:15) and thus cannot be described. God is also spirit (2 Cor 3:18) about which we know nothing. God is nowhere described in Scripture so we know nothing about His body, assuming that is even meaningful.
The only things we know for sure are some details of God's character, namely that He is loving, kind, holy, pure, gracious, forgiving, patient, etc, etc.
Therefore, I will not speculate.
In the specific case of Jer 13:17 we find a very famous passage, one of at least two where the prophet weeps. These have given Jeremiah the title: "The Weeping Prophet".
- Jer 13:17 - But if you do not listen, I will weep in secret because of your pride. My eyes will overflow with tears, because the LORD’s flock has been taken captive.
- Jer 9:1 - Oh, that my head were a spring of water, and my eyes a fountain of tears! I would weep day and night over the slain daughter of my people.
- Jer 9:10 - I will take up a weeping and wailing for the mountains, a dirge over the wilderness pasture, for they have been scorched so no one passes through, and the lowing of cattle is not heard. Both the birds of the air and the beasts have fled; they have gone away.
Note Ellicott's remarks:
(17) My soul shall weep in secret places for your pride.—The words present no difficulty that requires explanation, but deserve to be
noted in their exquisite tenderness as characteristic of the prophet’s
temperament (comp. Lamentations 1:16), reminding us of the tears shed
over Jerusalem (Luke 19:41) and of St. Paul’s “great heaviness and
continual sorrow” (Romans 9:2). Nothing remained for one who found his
labours fruitless but silent sorrow and intercession. The “secret
places” find a parallel in our Lord’s withdrawal for prayer into a
“solitary place” (Mark 1:35).
Thus it is in Jer 13:17 it is the prophet weeping, not God. However, we find many other passages where God expresses emotion, but this another question.