HorseAutoGallop - requires AdvancedMacros 7.10.0wd_pre136 from WD_fix fork build. (Find it in AM's #creations or `gradlew build` it yourself from my repo)

gallop.lua

-- bind to keypress MOSE:4
-- halts movement till sound comes back
-- prevents kicking caused by outrunning server
-- basically waits for getting sound packets back

local player, horse, last_gallop, action, x, y, z, a, b, c, hi, lo, last
local unpack, format, sqrt = table.unpack, string.format, math.sqrt
local waitTick, runOnMC, getPlayer = waitTick, runOnMC, getPlayer

local logdel, gal = logdel, 420780262
local notify = hud2D.actionbar

player = getPlayer()
horse = player.entityRiding
if not horse then
    logdel(gal,"&4[G] Gallop has no horse")
    return
end

if gallop_loop then
    gallop_loop = false
    logdel(gal,"&6[G] Gallop utility disabled")
else 
    gallop_loop = true
    logdel(gal,"&6[G] Gallop utility enabled")
    if velo_inlo then return end
end

hi, lo = 0, math.huge
local minmax = function(d)
    if hi < d then hi = d end
    if lo > d then lo = d end
    return d
end

local distance = function(snd, hors)
    local a, b, c = unpack(snd.pos)
    local x, y, z = unpack(hors.pos)
    a, b = x - a, z - c -- horizontal
    -- log("dst: ", math.abs(a), " ", math.abs(b))
    return math.sqrt(a*a + b*b)
end

local update = function()
    -- check if we are still a rider
    player = getPlayer()
    horse = player.entityRiding
    if not horse then
        gallop_loop = false
        logdel(gal+1,"&4[G] Gallop has no horse")
        return
    end

    -- initialise movement
    if not action then
        action = true
        forward(-1)
    end

    -- check first sound
    local gallop = gallop
    if not gallop then
        -- velocity not reached
        -- or loop not initialised
        return
    end

    -- display debug info in actionbar
    local d = distance(gallop, horse) -- current distance
    local d_, hi_ = format("%.3f",d), format("%.3f",hi)
    notify("&6Distance: "..format("%.3f",last).. " &7["..hi_.."]")
    -- notify("&6Distance: "..d_.." &7["..hi_.."]") -- too frequent

    if last_gallop then -- if loop is ready
        -- update distance range
        if gallop ~= last_gallop then
            last = minmax(distance(last_gallop,gallop))
        end

        -- check for latest sound update
        if gallop == last_gallop and hi ~= 0 then
            -- no sound update was there
            --if d > 1.4142 * hi then
            --if d > 2.236 * hi then
            --if d > 13 then
            if d > 16 then -- this value is tweakable
                logdel(gal+1,"&4[G] LAGSPIKE? Reached: "..d_.."m")
                notify("&4Distance: "..d_.." &7["..hi_.."]")
                playSound("pop.wav").loop(1)
                action = false
                gallop = false
                _G.gallop = false
                gallop_await = true
                last_gallop = false
                forward(0)
            end
            return
        end
    end

    last_gallop = gallop
end

-- state machine
last = 0
action = false
gallop = false
_G.gallop = false
gallop_await = false
last_gallop = false

-- execution loop
local wasWaiting = false
while gallop_loop do
    -- check if we are still a rider
    player = getPlayer()
    horse = player.entityRiding
    if not horse then
        gallop_loop = false
        logdel(gal+1,"&4[G] Gallop has no horse")
        break
    end

    if not gallop_await then
        if wasWaiting then
            sleep(1000)
            wasWaiting = false
        end
        runOnMC(update)
    else
        wasWaiting = gallop_await
    end
    waitTick()
end
forward(0)

gallop_forward.lua

-- bind to keypress MOUSE:3
-- autowalks again if you unpress it by accident

local player = getPlayer()
local horse = player.entityRiding
if horse then
    forward(-1)
    logdel(420780264) -- delete message by unique ID, if exists
    return
else
    logdel(420780264,"&4You are not riding anything!")
end

gallop_sound.lua

-- bind to event Sound
-- other script part uses global variable
-- `gallop` sourced from this execution

local _, _, name, sound, control = ...
-- sound.category == "neutral" and 
if name == "minecraft:entity.horse.gallop" then
    gallop = sound -- table describing sound
    gallop.time = os.millis() -- current time
    gallop_await = false
end