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.
for (const std::pair<uint256, CWalletTx>& pairWtx : pwallet->mapWallet) {
        CWalletTx tx = pairWtx.second;
        if (depth == -1 || tx.GetDepthInMainChain() < depth) {
            ListTransactions(pwallet, tx, "*", 0, true, transactions, filter);
        }
    }
    
    
    UniValue removed(UniValue::VARR);
    while (include_removed && paltindex && paltindex != pindex) {
        CBlock block;
        if (!ReadBlockFromDisk(block, paltindex, Params().GetConsensus())) {
            throw JSONRPCError(RPC_INTERNAL_ERROR, "Can't read block from disk");
        }
        for (const CTransactionRef& tx : block.vtx) {
            auto it = pwallet->mapWallet.find(tx->GetHash());
            if (it != pwallet->mapWallet.end()) {
                
                
                ListTransactions(pwallet, it->second, "*", -100000000, true, removed, filter);
            }
        }
        paltindex = paltindex->pprev;
    }
    CBlockIndex *pblockLast = chainActive[chainActive.Height() + 1 - target_confirms];
    uint256 lastblock = pblockLast ? pblockLast->GetBlockHash() : uint256();
    UniValue ret(UniValue::VOBJ);
    ret.push_back(Pair("transactions", transactions));
    if (include_removed) ret.push_back(Pair("removed", removed));
    ret.push_back(Pair("lastblock", lastblock.GetHex()));