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.
"Issuing the walletpassphrase command while the wallet is already unlocked will set a new unlock\n"
            "time that overrides the old one.\n"
            "\nExamples:\n"
            "\nUnlock the wallet for 60 seconds\n"
            + HelpExampleCli("walletpassphrase", "\"my pass phrase\" 60") +
            "\nLock the wallet again (before 60 seconds)\n"
            + HelpExampleCli("walletlock", "") +
            "\nAs json rpc call\n"
            + HelpExampleRpc("walletpassphrase", "\"my pass phrase\", 60")
        );
    }
    LOCK2(cs_main, pwallet->cs_wallet);
    if (request.fHelp)
        return true;
    if (!pwallet->IsCrypted()) {
        throw JSONRPCError(RPC_WALLET_WRONG_ENC_STATE, "Error: running with an unencrypted wallet, but walletpassphrase was called.");
    }
    
    SecureString strWalletPass;
    strWalletPass.reserve(100);
    
    
    strWalletPass = request.params[0].get_str().c_str();
    
    int64_t nSleepTime = request.params[1].get_int64();
    
    if (nSleepTime < 0) {
        throw JSONRPCError(RPC_INVALID_PARAMETER, "Timeout cannot be negative.");
    }