There are 3 ways that DVC villas become available for cash reservations by non-members:
1) Disney retains ownership of a very small percentage (< 10%) of the room inventory at each DVC resort. You'll see these available for cash reservations. I'm not sure exactly when these become available, I'd guess sometime between 7-11 months out. When a new DVC resort is in the sales process, there's also a lot of developer inventory in DVC's possession - the percentage of the resort's room inventory that has not been sold to members. A good bit of this is also often available for cash reservations.
2) If members trade out of the DVC system, for instance to stay at DLP, or a non-DVC resort at DL or WDW, or take an ABD trip, or a
DCL cruise, a villa of roughly equal 'value' is sent from the member inventory to be rented for cash to cover the cost of the trade. These don't appear in any particular time frame, just whenever a member trades out.
(The seven month window referred to by a PP is not really relevant in this situation. When a BLT member uses their points to stay at another DVC resort, like Aulani, a BLT villa does not go into the cash inventory. That's only when members stay at NON-DVC resorts.)
3) At 60 days out, any DVC villas not reserved by members go into the cash inventory to recover breakage income for that resort's owners. The difference with this example is, if a member then comes along and wants to rent one of these with their points, it gets pulled back out of the cash inventory and goes back to member inventory.
OP, the upshot of all this is that you just have to keep watching for BLT villas to appear in the cash inventory. There's really no hard and fast rule for when you'll see one appear.