I think it doesn't matter which way the gift is made. Whether your brother signs the deed before probate or after it, he is making a gift to you. If
the gift is worth over $13,000, a federal gift tax return is supposed to be filed. However, the current federal gift tax exemption is $5 million dollars. No tax is due if the total lifetime value of gifts made by the giver is less than $5 million. It seems extremely unlikely that his half-share in the house is worth over $5 million.
If you do decide to file a gift tax return, it seems fair to me that you, not your brother, pay to have ti prepared. Though he would have to sign it and file it.
Only a few states impose gifts taxes. I do not know if the house is in a state that does impose gift taxes. Even if it is, these taxes are likely to be minor at worst. If state gift taxes are assessed, it seems right that you, not your brother, pay them.