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.
{
    CAmount nFee;
    std::string strSentAccount;
    std::list<COutputEntry> listReceived;
    std::list<COutputEntry> listSent;
    wtx.GetAmounts(listReceived, listSent, nFee, strSentAccount, filter);
    bool fAllAccounts = (strAccount == std::string("*"));
    bool involvesWatchonly = wtx.IsFromMe(ISMINE_WATCH_ONLY);
    
    if ((!listSent.empty() || nFee != 0) && (fAllAccounts || strAccount == strSentAccount))
    {
        for (const COutputEntry& s : listSent)
        {
            UniValue entry(UniValue::VOBJ);
            if (involvesWatchonly || (::IsMine(*pwallet, s.destination) & ISMINE_WATCH_ONLY)) {
                entry.push_back(Pair("involvesWatchonly", true));
            }
            entry.push_back(Pair("account", strSentAccount));
            MaybePushAddress(entry, s.destination);
            entry.push_back(Pair("category", "send"));
            entry.push_back(Pair("amount", ValueFromAmount(-s.amount)));
            if (pwallet->mapAddressBook.count(s.destination)) {
                entry.push_back(Pair("label", pwallet->mapAddressBook[s.destination].name));
            }
            entry.push_back(Pair("vout", s.vout));
            entry.push_back(Pair("fee", ValueFromAmount(-nFee)));
            if (fLong)
                WalletTxToJSON(wtx, entry);
            entry.push_back(Pair("abandoned", wtx.isAbandoned()));
            ret.push_back(entry);