Phasing into the trough over eight quarters vs just funding the sleeve now

I have a target allocation of about 12% to listed real estate and roughly $400k to move into it. My default is a slow build, equal tranches over eight quarters, because I do not trust myself to call the bottom of a valuation gap that is already described as historically wide.

What is bothering me is that the argument for deploying here is specifically about a discount closing. If the discount closes in two quarters, a phased build puts most of the money in after the move, and I have paid for comfort with the entire thesis. If rates back up 100bp first, the phased build looks smart.

So the phasing decision is really a bet on the shape of the rerating rather than the direction. Two things I cannot resolve. First, the dividend yield keeps accruing while I sit in cash, and the spread between a REIT sleeve's yield and short-term cash is thinner than it usually is in a trough, which weakens the cost-of-waiting argument. Second, if I phase, do I phase into the same sector weights each time, or do I hold the tactical tilts (data centers, industrial) for later tranches and start with the boring diversified core?

Has anyone built a rule for this that survived contact with a quarter where prices moved 9% before the next tranche date?