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.
}
    EnsureWalletIsUnlocked(pwallet);
    pwallet->TopUpKeyPool(kpSize);
    if (pwallet->GetKeyPoolSize() < kpSize) {
        throw JSONRPCError(RPC_WALLET_ERROR, "Error refreshing keypool.");
    }
    return NullUniValue;
}
static void LockWallet(CWallet* pWallet)
{
    LOCK(pWallet->cs_wallet);
    pWallet->nRelockTime = 0;
    pWallet->Lock();
}
UniValue walletpassphrase(const JSONRPCRequest& request)
{
    CWallet * const pwallet = GetWalletForJSONRPCRequest(request);
    if (!EnsureWalletIsAvailable(pwallet, request.fHelp)) {
        return NullUniValue;
    }
    if (request.fHelp || request.params.size() != 2) {
        throw std::runtime_error(
            "walletpassphrase \"passphrase\" timeout\n"
            "\nStores the wallet decryption key in memory for 'timeout' seconds.\n"
            "This is needed prior to performing transactions related to private keys such as sending bitcoins\n"
            "\nArguments:\n"
            "1. \"passphrase\"     (string, required) The wallet passphrase\n"
            "2. timeout            (numeric, required) The time to keep the decryption key in seconds. Limited to at most 1073741824 (2^30) seconds.\n"
            "                                          Any value greater than 1073741824 seconds will be set to 1073741824 seconds.\n"
            "\nNote:\n"