Avoiding tax on investment draw/ repayment

No such thing as a tax-free rollover for taxable investment accounts.

Maybe he could borrow against the investment account. But this is expensive.

Define "investment" account?  Is it a retirement account?

"pulling some extra out of his investment this year"

For investments, the amount taken isn't by default taxable. The Gain would be taxable. Amount from sales minus Basis = Gain. And if it's long term, it's taxed differently than ordinary income.

"selling his current home and have cash flow coming from that sale"

If he meets the eligibility factors, he can exclude up to $250,000 gain from taxes, or $500,000 if he is married and they both are eligible.

"Can he replace the investment draw in order to avoid the taxation on it?"

If it is just money, there is no tax on drawing your own money. If it requires selling or other closing out of the investment type, then it would be evaluated to see if it is a taxable transaction.

"It seems so basic"

The specifics matter. Your wording is very vague.

There is a 60 day window to return funds to an IRA account that was withdrawn from an IRA account

Is that the information you are looking for?