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.
"At a minimum, the new fee rate must be high enough to pay an additional new relay fee (incrementalfee\n"
            "returned by getnetworkinfo) to enter the node's mempool.\n"
            "\nArguments:\n"
            "1. txid                  (string, required) The txid to be bumped\n"
            "2. options               (object, optional)\n"
            "   {\n"
            "     \"confTarget\"        (numeric, optional) Confirmation target (in blocks)\n"
            "     \"totalFee\"          (numeric, optional) Total fee (NOT feerate) to pay, in satoshis.\n"
            "                         In rare cases, the actual fee paid might be slightly higher than the specified\n"
            "                         totalFee if the tx change output has to be removed because it is too close to\n"
            "                         the dust threshold.\n"
            "     \"replaceable\"       (boolean, optional, default true) Whether the new transaction should still be\n"
            "                         marked bip-125 replaceable. If true, the sequence numbers in the transaction will\n"
            "                         be left unchanged from the original. If false, any input sequence numbers in the\n"
            "                         original transaction that were less than 0xfffffffe will be increased to 0xfffffffe\n"
            "                         so the new transaction will not be explicitly bip-125 replaceable (though it may\n"
            "                         still be replaceable in practice, for example if it has unconfirmed ancestors which\n"
            "                         are replaceable).\n"
            "     \"estimate_mode\"     (string, optional, default=UNSET) The fee estimate mode, must be one of:\n"
            "         \"UNSET\"\n"
            "         \"ECONOMICAL\"\n"
            "         \"CONSERVATIVE\"\n"
            "   }\n"
            "\nResult:\n"
            "{\n"
            "  \"txid\":    \"value\",   (string)  The id of the new transaction\n"
            "  \"origfee\":  n,         (numeric) Fee of the replaced transaction\n"
            "  \"fee\":      n,         (numeric) Fee of the new transaction\n"
            "  \"errors\":  [ str... ] (json array of strings) Errors encountered during processing (may be empty)\n"
            "}\n"