My 13month old is also always on the go and does not play much with toys.
What he does like is....
emptying and filling things - he has a make up bag in the bathroom filled with plastic bottles and containers which will keep him busy for a while.
posting things - especially through the stairgate and over the fire guard
chasing the cats
opening / shutting / emptying cupboards then climbing inside of them
crawling around carrying things in his hands
books especially board books with either flaps, textures or photographs
shaking things especially plastic bottles filled with water, pasta, lentils, etc
mobile phones and remote controls (carrying them, posting them, talking on them)
playing with shoes, especially those with laces
playing with pebbles (although he will often try and eat them)
ripping paper (again he will try and eat it)
belts, ribbons, toy snakes - although I closely moniter him as he does put them round his neck
playing with saucepans, wooden spoons, plastic containers etc
He absolutely adored a helium balloon on a long piece of ribbon with a weight but again their was the strangling problem - but he was happy!
If he is having a funny five minutes, I will find some of his toys and play with them properly and enthusiastically and ignore him. Often he will come over and join in. Occasionally he will build with bricks, push cars along or press the buttons on his musical toys.
If we are desperate the tele will keep him happy for a little while - he likes the music channels!
All of the above will occupy him for a few minutes if I am lucky and if he goes quiet I know that he has got into mischief! It is a constant battle and exhausting so often I give him things which I proberbly shouldn't