Brain-Flak, 60 bytes

{({}<>)<>}<>{(({}<>)<>[({})]){((<{}>))}{}{({}<>{})(<>)}{}}<>

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###Explanation:

{({}<>)<>}<>   Reverse stack

{   While input exists
  (
    ({}<>)   Push copy of last element to the other stack
    <>[({})] And subtract a copy of the next element
  )   Push the difference
  {   If the difference is not 0
    ((<{}>)) Push two zeroes
  }{}  Pop a zero
  {   If the next element is not zero, i.e the identical element
    ({}<>{})  Add the element to the copy of the previous element
    (<>)      Push a zero
  }{}    Pop the zero
}<>  End loop and switch to output stack

Brain-Flak, 60 bytes

{({}<>)<>}<>{(({}<>)<>[({})]){((<{}>))}{}{({}<>{})(<>)}{}}<>

Try it online!

Explanation:

{({}<>)<>}<>   Reverse stack

{   While input exists
  (
    ({}<>)   Push copy of last element to the other stack
    <>[({})] And subtract a copy of the next element
  )   Push the difference
  {   If the difference is not 0
    ((<{}>)) Push two zeroes
  }{}  Pop a zero
  {   If the next element is not zero, i.e the identical element
    ({}<>{})  Add the element to the copy of the previous element
    (<>)      Push a zero
  }{}    Pop the zero
}<>  End loop and switch to output stack