Player wont stay on moving part using BodyMovers?

I made a script that allows a part to move between two parts using BodyPosition. However, when the part moves, the player doesn't move with it, and instead just falls off.

local movePart = script.Parent
local startPart = movePart.Parent.StartPart
local endPart = movePart.Parent.EndPart
local bodyPosition = movePart.BodyPosition

movePart.BodyGyro.CFrame = movePart.CFrame

while true do
	bodyPosition.Position = startPart.Position
	wait(5)
	bodyPosition.Position = endPart.Position
	wait(5)
end

GIF to show what I mean: https://gyazo.com/4b4d7592ffcc81861917d49829e1b3fd

try changing from this

local movePart = script.Parent
local startPart = movePart.Parent.StartPart
local endPart = movePart.Parent.EndPart
local bodyPosition = movePart.BodyPosition

movePart.BodyGyro.CFrame = movePart.CFrame

while true do
    bodyPosition.Position = startPart.Position
    wait(5)
    bodyPosition.Position = endPart.Position
    wait(5)
end

to this

local movePart = script.Parent
local startPart = movePart.Parent.StartPart
local endPart = movePart.Parent.EndPart
local bodyPosition = movePart.BodyPosition

while true do
    bodyPosition.Position = startPart.Position
    wait(5)
    bodyPosition.Position = endPart.Position
    wait(5)
end