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.
{
    CWallet * const pwallet = GetWalletForJSONRPCRequest(request);
    if (!EnsureWalletIsAvailable(pwallet, request.fHelp)) {
        return NullUniValue;
    }
    if (request.fHelp || request.params.size() != 1)
        throw std::runtime_error(
            "backupwallet \"destination\"\n"
            "\nSafely copies current wallet file to destination, which can be a directory or a path with filename.\n"
            "\nArguments:\n"
            "1. \"destination\"   (string) The destination directory or file\n"
            "\nExamples:\n"
            + HelpExampleCli("backupwallet", "\"backup.dat\"")
            + HelpExampleRpc("backupwallet", "\"backup.dat\"")
        );
    
    
    pwallet->BlockUntilSyncedToCurrentChain();
    LOCK2(cs_main, pwallet->cs_wallet);
    std::string strDest = request.params[0].get_str();
    if (!pwallet->BackupWallet(strDest)) {
        throw JSONRPCError(RPC_WALLET_ERROR, "Error: Wallet backup failed!");
    }
    return NullUniValue;
}
UniValue keypoolrefill(const JSONRPCRequest& request)