If I unlock an encrypted wallet for 359711509437336256 or less seconds, I can sign transactions with it:

    $ bitcoin-cli walletpassphrase "$x" 359711509437336256
    $ echo $?
    0
    $ bitcoin-cli signrawtransaction $tx | grep complete
      "complete": true

But if I unlock it for 359711509437336257 or more seconds, it appears to have unlocked but I can't sign any transactions:

    $ bitcoin-cli walletpassphrase "$x" 359711509437336257
    $ echo $?
    0
    $ bitcoin-cli signrawtransaction $tx | grep complete
    error code: -13
    error message:
    Error: Please enter the wallet passphrase with walletpassphrase first.

I don't know the significance of that number. It's nowhere near a power of 2.

I was trying to unlock the wallet effectively "forever", so put a big number. If I use too big a number (2^63 or more) I get an error message `JSON integer out of range` but for numbers between 359711509437336257 and 2^63-1 inclusive I get no error, but no actual unlocking.
{
    if (request.URI.substr(0, WALLET_ENDPOINT_BASE.size()) == WALLET_ENDPOINT_BASE) {
        
        std::string requestedWallet = urlDecode(request.URI.substr(WALLET_ENDPOINT_BASE.size()));
        for (CWalletRef pwallet : ::vpwallets) {
            if (pwallet->GetName() == requestedWallet) {
                return pwallet;
            }
        }
        throw JSONRPCError(RPC_WALLET_NOT_FOUND, "Requested wallet does not exist or is not loaded");
    }
    return ::vpwallets.size() == 1 || (request.fHelp && ::vpwallets.size() > 0) ? ::vpwallets[0] : nullptr;
}
std::string HelpRequiringPassphrase(CWallet * const pwallet)