"In the context of the SOS Redouble, when it's described as a "long minor", it suggests that the redoubling player has length (often 6+ cards) in one or both of the minor suits (clubs or diamonds) and very few points. They are likely distributional with shortness in one or both of the major suits, and are uncomfortable with the contract at 1NT, even more so when it's doubled.
The player is essentially asking their partner to escape to their longest minor suit, hoping that the partner has some length in one or both minors. It's a way of trying to find a safer contract in a situation where the player expects to be heavily penalized if they stay in 1NT doubled.
In response to this, as the 1NT bidder, you should bid your longest minor suit, even if it's not particularly strong. If you have equal length in both minors, you might prefer to bid clubs, as it leaves more room for further bidding if necessary.
Remember, this SOS redouble is not a strength showing bid, it's a distributional bid. It is important for you to identify your best minor to give your partnership the best chance to find a suitable contract."

Note - it took a bit of prompting to get there