To (or ‘towards') you my heart said,
“Seek you my face”,
It is tempting here to see these words as the words of YHWH interspersed with the Psalmist's own words, or put into the Psalmist's mouth, so that it is the heart of YHWH speaking to his heart, and saying ‘Seek My face'. And that fits best with what follows. On the other hand, the general impression of the Hebrew is rather that they are the words of the Psalmist, in which case they refer to a desperate heart plea to YHWH to seek him out and look into his face when no one else will do so. All have turned away from him, including his family, but he still hopes that YHWH will seek him out and look him in the face, as he intends to look YHWH in the face.
“Your face, YHWH, will I seek,
Hide not your face from me.”
But whatever the situation he intends to seek the face of YHWH, and so he prays that YHWH will not hide His face from him. The heart rending nature of the situation is clearly apparent, and brought out by the stuttering metre.
Put not your servant away in anger,
You have been my help,
Cast me not off, nor forsake me,
O God of my salvation.
He continues his theme. Though all have turned against him he prays that YHWH will not turn against him, for it is ever YHWH Who has been his help, and if He were to turn from him what would he have left? So he pleads with Him not to cast him off or forsake him, and to remember that He is the God Who saves, and Who saves him, as he has already stated in Psalms 27:1. That being so he throws himself on Him. It reveals something of how deserted he feels. When all others have cast him off, YHWH is his last hope.