What is the origin of closing one's eyes during prayer? I have been a Christian since my youth, but I have never received a satisfactory answer to this question.
Why must a Christian close their eyes during prayer?
In large services in the west, (I am not familiar with other traditions) believers bow their heads and close their eyes while being led in prayer, often speaking internally to God or self reflecting. Bowing one's head, or prostrating themselves is itself a form of worship.
Personally, in moments of personal prayer I do not close my eyes because I find it more distracting. But in my family and church I grew up in this would be seen as very offensive if someone might walk in and see me praying with my eyes open.
I'm mostly interested in the scriptural basis for closing one's eyes while praying. Not so much the historical reason for the tradition developing, although I recognize it might be difficult to separate the two.
Closing the eyes in prayer is for the same reason as one may fast in association with prayer.
It is to detach oneself from the things of this world, from the things of the flesh and from the things that can be seen.
But, like fasting, it is purely voluntary. There are no 'instructions' as to when to pray, or how often to pray anywhere in the bible (only examples to follow, if one  wishes).
Nor are there 'instructions' about fasting. It is purely voluntary, though it is encouraged in scripture and, again, there are examples to follow.
Likewise there are examples to follow, round about us, as to closing the eyes. Every congregation I have ever worshiped with, has done so.
And so do I, personally, every time I 'shut my closet door' and pray to the Father in secret, where none else can see me.