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.
std::set<CTxDestination> destinations;
    std::vector<CRecipient> vecSend;
    CAmount totalAmount = 0;
    std::vector<std::string> keys = sendTo.getKeys();
    for (const std::string& name_ : keys) {
        CTxDestination dest = DecodeDestination(name_);
        if (!IsValidDestination(dest)) {
            throw JSONRPCError(RPC_INVALID_ADDRESS_OR_KEY, std::string("Invalid Bitcoin address: ") + name_);
        }
        if (destinations.count(dest)) {
            throw JSONRPCError(RPC_INVALID_PARAMETER, std::string("Invalid parameter, duplicated address: ") + name_);
        }
        destinations.insert(dest);
        CScript scriptPubKey = GetScriptForDestination(dest);
        CAmount nAmount = AmountFromValue(sendTo[name_]);
        if (nAmount <= 0)
            throw JSONRPCError(RPC_TYPE_ERROR, "Invalid amount for send");
        totalAmount += nAmount;
        bool fSubtractFeeFromAmount = false;
        for (unsigned int idx = 0; idx < subtractFeeFromAmount.size(); idx++) {
            const UniValue& addr = subtractFeeFromAmount[idx];
            if (addr.get_str() == name_)
                fSubtractFeeFromAmount = true;
        }
        CRecipient recipient = {scriptPubKey, nAmount, fSubtractFeeFromAmount};
        vecSend.push_back(recipient);
    }
    EnsureWalletIsUnlocked(pwallet);
    
    CAmount nBalance = pwallet->GetLegacyBalance(ISMINE_SPENDABLE, nMinDepth, &strAccount);