I think that in song leading, there are 2 things going on. First, the leader is indeed worshipping God individually, and I think needs to be sincere and to sing from the heart. People in the congregation take their lead from this, and join in. When we all do that together, our worship takes on one aspect of its corporate dimension.
In that sense, I am not too fussed about eyes closed, hands clapping or in the air. I’m much more interested in the person displaying an overall appearance that is convincing! (eg smiles in songs of joy, reflective looks in reflective songs etc). A parallel example might be leading the congregation in prayer, where your own physical approach to prayer will help people in their prayer. Some do it with eyes open, others with eyes closed.
The second thing that’s going on for songleaders though is a communication with the congregation. Not only are we expecting them to copy us, but we’re also deliberately trying to get a message across to people. Music is a ministry of proclaiming the word, in a similar but not identical way to preaching, or bible reading. I reckon that in this aspect of the role we benefit from eyes open, since it’s hard to communicate to someone in front of you when your eyes are closed. I do sometimes find it difficult when I’m in a congregation to engage with the song leaders if they’re closing their eyes to me.
To make the point another way, another important aspect of our corporate worship is the actual focus on our togetherness. In our awareness and engaging with each other, we build one another up in the truths of the gospel. When we do this, God is worshipped, a point that the New Testament makes very clear (eg the sheep and the goats story in Matt 25, where in serving Jesus’ brothers, you are serving Jesus himself).
My own practice is that my eyes will be open and shut at different times when I sing, depending on the situation. If I’m doing an item, especially one that is personal and individual, often I’ll sing with my eyes shut, but never for the whole song, because I still feel that there’s a communication element to it. Most congregational songs I’ll have my eyes open for the majority of it, but at times when I’m particularly aware of God’s interest in me personally, my eyes will shut for parts of it.
At my own church, I don’t tend to make rules about what people can and can’t do. This seems to me to be unnecessary and can I think smother the ministry of music! We try to think about what we’re actually doing when we lead singing, and leave it to individual songleaders to make up their minds.