[Fizzlemizz]

I heard it sing only today. Maybe the time between songs is just longer randoms.

If you (and just you) wanted to hear it more often you could use something like:
The min/max times can be set to whatever doesn't annoy you (8, 12 seconds is very short but you don't have to wait long to test.)

-- More music for Sunflower pet
local minTime, maxTime = 8, 12 -- min/max times between songs in seconds
local castID = 93823
local guids = { -- add additional guids here
    ["BattlePet-0-0000121FED47"] = true, 
    ["BattlePet-0-0000121FED42"] = true,
}
local soundIDs = {
    567354,
    567327,
    567317,
    567338,
    567374,
    567295,
}
local summoned
local function SingFlowerSing()
    local id = C_PetJournal.GetSummonedPetGUID()
    if not guids[id] then
        summoned = false
        return
    end
    PlaySoundFile(soundIDs[random(1, #soundIDs)])      
    C_Timer.After(random(minTime, maxTime), SingFlowerSing)
end
local f = CreateFrame("Frame")
f:RegisterUnitEvent("UNIT_SPELLCAST_SUCCEEDED", "player")
f:RegisterUnitEvent("UNIT_LEVEL", "player")
f:RegisterEvent("PLAYER_ENTERING_WORLD")
f:SetScript("OnEvent", function(self, event, ...)
    local unit, _, spellid = ...
    if event == "UNIT_SPELLCAST_SUCCEEDED" and spellid == castID then
        if not summoned then
            summoned = true
            C_Timer.After(random(minTime, maxTime), SingFlowerSing)
        end
    elseif event == "PLAYER_ENTERING_WORLD" or event == "UNIT_LEVEL" then
        local id = C_PetJournal.GetSummonedPetGUID()
        if guids[id] then
            self:GetScript("OnEvent")(self, "UNIT_SPELLCAST_SUCCEEDED", "player", nil, castID)
            self:UnregisterEvent("UNIT_LEVEL")
        end
        self:UnregisterEvent("PLAYER_ENTERING_WORLD")
        if event == "UNIT_LEVEL" then
            self:UnregisterEvent("UNIT_LEVEL")
        end
    end
end)

Copy/paste the code to the website addon.bool.no to create download as an addon.