Replace targetTweetId, targetTweetTimestamp (remove the ·), cookie, CSRF_TOKEN (in headers) and ACCESS_TOKEN (also in headers).

twitterLikePicker.js

const request = require("request-promise-native"),
    fs = require("fs")

const targetTweetId = "1186731922766159872",
    targetTweetTimestamp = new Date("9:50 PM Oct 22, 2019"),
    cookie = "auth_token=; ct0=CSRF_TOKEN"

const twitter = request.defaults({
    baseUrl: "https://api.twitter.com/",
    headers: {
        "Accept": "text/plain, */*; q=0.01",
        "Authorization": "Bearer ACCESS_TOKEN",
        "Origin": "https://tweetdeck.twitter.com",
        "Referer": "https://tweetdeck.twitter.com/",
        "Sec-Fetch-Mode": "cors",
        "User-Agent": "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/76.0.3809.132 Safari/537.36",
        "X-Csrf-Token": "CSRF_TOKEN",
        "X-Twitter-Auth-Type": "OAuth2Session",
        cookie
    }
})

const actionsQuery = {
    "model_version": "7",
    "count": "40",
    "skip_aggregation": "true",
    "cards_platform": "Web-13",
    "include_entities": "1",
    "include_user_entities": "1",
    "include_cards": "1",
    "send_error_codes": "1",
    "tweet_mode": "extended",
    "include_ext_alt_text": "true",
    "include_reply_count": "true",
}

const wait = ms => new Promise(res => setTimeout(res, ms))

let entries = []

async function getActions(maxId="") {
    maxId
    ? actionsQuery.max_id = maxId
    : delete actionsQuery.max_id

    let cachedEntries = entries.length

    const response = await twitter.get("1.1/activity/about_me.json", {
        qs: actionsQuery
    })
    .then(JSON.parse)

    response.forEach(action => {
        if (action.action == "favorite" && action.targets[0].id_str == targetTweetId) {
            entries.push({
                name: action.sources[0].name,
                id: action.sources[0].screen_name
            })
        }
    })

    if (new Date(response[response.length - 1].created_at) < targetTweetTimestamp) {
        console.log(`Went through all entries. Total: ${entries.length}`)
        return entries
    } else {
        console.log(`Added ${entries.length - cachedEntries} entries. Total: ${entries.length}. Fetching more...`)
        await wait(200)
        return await getActions(Number(response[response.length - 1].max_position) +1)
    }
}

async function main() {
    const things = await getActions()
    things.forEach(e => console.log(`${e.name} (${e.id})`))
    fs.writeFileSync("likes.json", JSON.stringify(things))
}

main()