One day Otis spilt some milk on the kitchen floor. 'I'll just go get my mop' he said to me and off he went. He cleaned up the milk and put his mop away. He was two. I totally credit his school (and teachers) for this as he had recently started in a formal Montessori classroom.
I guarantee you cleaning up after accidentally making a spill or breakage happens naturally, automatically to children (including toddlers) in Montessori environments all around the world - everyday. Often in Montessori schools using a mop or wet mopping is actually presented as a lesson. Not to say that Otis always cleans up his spills (he doesn't) but what (to me!) is miraculous is that at two years old he could recognise a spill and without even thinking collect the materials and clean it up. This can only happen when and where the environment allows for it.
A child is much less likely to clean up if his materials are out of reach, he doesn't know which cloth to use, if he has to ask for help.
It's not just about independence. It is also about self pride. Contributing to a community. Doing a job/task well. Completing a job/task from start to finish. About being a responsible person. It is about respecting a child enough to allow them to clean up after themselves.
Our cleaning station as pictured above is located in a small cupboard under our stairs. It is the same area where I keep my broom and mop and our vacuum cleaner and buckets. Previously we stored the children's cleaning materials in and near the kitchen. We still need cleaning cloths and a spray bottle in the kitchen kept on the pantry shelves, but where the materials are located really depends on each family and each home.
A children's cleaning station isn't just for children in the sensitive period for practical life. It's for all children. In the sensitive period or not children need to have access to their materials. Caspar (now 7) doesn't particularly gain enjoyment (but perhaps satisfaction) from cleaning (as Otis does) but still needs to be able to find and reach a broom or dustpan for when he needs to clean up a breakage or spill.