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Investment Signal Breadth Across Sectors

Let's assume there is a mandate to create a long only portfolio that matches the sector exposures of some investable benchmark. Assuming such would require the portfolio to hold at least 1 (likely more for diversification's sake, but not necessarily for theoretical purposes) security per each of the GICS sectors (11 sectors in total with the recent addition of Real Estate).

Let's also assume we have some investment signal that we believe is predictive of future excess return. For simplicity's sake, say it is some linear combination of market cap and liquidity.

How does the community consider taking said signal, which may very well be sector biased (i.e. could be very predictive for information technology sector, but much less so for health care) and defining the number of securities to capture per sector? One solution could be to take the top 3 securities by sector, but it completely ignores the possible differences in efficacy of your signal across sectors.

Portfolio Constraints / Goals

Long Only

At least 11 securities (1 for each GICS sector)

Maintain Sector Neutral to a Benchmark

Portfolio will trade ~4 times per year

Maximize Information Ratio

Relevant Questions to Define Thought Process

What metrics would you use to define breadth?

Would it be a rolling window or a static number through time (i.e. perhaps you believe when trailing 1 year security return dispersion is highest within a sector, you want to take more bets to diversify)?