Turning it into a choice of whether to positively qualify for the rebate certainly seems to transform the question into one of affirmative volition, rather than latent inaction. At least I think that is what the hypothetical is aiming at. Also, wrapping up the tax-penalty in the framework of the income tax adds a layer of complication onto things, making it that much more difficult to identify the tax-penalty as one or the other (or both). At its core though, I don't see the situation as being very different, since the additional tax-penalty (now piggybacked onto the income tax), is still hinging on an refusal to take special action. The default operation in both situations is that people will be losing additional money to the government, unless and until they go out of their way to avoid it.

The idea of a positive transaction being the touchstone of a properly-named "tax" takes the default operation to be that people won't be losing additional money to the government, unless and until something about the status quo changes.

Here's the way the situation looks to me, but I'd be happy to hear other ways of interpreting. At T1, I own my original house. At T2, the house has been sold (at a profit over my basis). At T3a, I have bought another house. On the other hand, at T3b, 18 months have passed, I haven't bought another house, and I must now pay a capital gains tax. At T1, the status quo is that I own a house (and, ignoring property taxes and everything, I won't have to pay any additional taxes on it). In moving to T2, I have upset the status quo by choosing to engage in an activity that brings with it a capital gains tax. The tax, therefore, is tied to the positive action of my earning money by selling something. If I go to T3a, the tax is forgiven on account of whatever policy aims that serves. If I go to T3b, then the tax comes due, and I must pay it. It can appear that the tax is only being forced upon me by virtue of my failure to buy another house, and maybe it is, from a certain viewpoint. At the same time, however, it shouldn't be forgotten that I found myself in T2 only as a result of my own choice to leave T1. The move from T2 to T3b is certainly the result of personal non-action, but is the tax excised on account of the move from T1 to T2, or the move from T2 to T3b? I gravitate toward the former, but what would Holmes say?