Okay so this passage doesn't say that when we sing praises, God's presence comes more fully. But doesn't God love our praises? Absolutely! So wouldn't it be a principle anyway, just from that common knowledge? Not really! Why stop at praise? Doesn't God love our love of others, our encouragement of others, our discipleship efforts, our evangelism, our diligence and excellence while working, our service in many and various forms, and so much more? Of course! So why would there be a special presence that singing brings about?

If anyone knew about this, Elijah did. Yet it was in fact the prophets of Baal that spent hours dancing and singing and worshipping to their god (1 Kings 18:26-29). To no effect. What did Elijah do? He just prayed a simple prayer, without formula:

Here's a more balanced principle: God is more likely to show up when his reputation is at stake. So when after singing we have a time where we exercise the gifts of the Spirit, I believe it has much more to do with the fact that we are making God potentially look silly if he doesn't come through, than the fact that we've sung to him. That's Elijah's appeal. That's Moses' appeal when God was going to wipe out Israel for worshipping a calf (Exodus 32:9-10): 'but others will mock you, saying, you led them out of Egypt to destroy them.' (32:11-13). God relented (32:14). It was Israel's path to victory time and again in the Promised Land—defeat through trumpets, not siege (Joshua 6); defeat by 300, not by might (Judges 7); defeat by the Lord: not man. God wants the glory! Yet still, each of these examples is based off God speaking to them and asking them to do it, not out of a higher principle that even God has to obey. So if he's promised something, we can remind him to fulfil it. Otherwise, like David and Jesus in Psalm 22, we should cry out to God for deliverance, but be prepared to accept persecution for higher purposes, and trust God anyway. That's maturity.

So there is no secret Scriptural principle that suggests God manifests himself more around praise. Does God love our praise and worship? Yes. But let's worship him out of love for him, not as some sort of magic conjuring trick. He's much more than a genie could ever be. In fact, he's the one who moves you to worship!