Shader - Remove Alpha before adding color

Hello, I am new to shaders and I am taking a shot out creating one. My idea is that the model itself would be invisible, but a rim around the model would glow. The problem that I am having is that reducing the alpha to zero makes both the model AND the emission dissapear. How do I make the model dissapear but leave the emmisive? Here is my shader:

 SubShader {
         Tags { "Queue"="Transparent" "RenderType"="Transparent" }
         LOD 200
         
         CGPROGRAM
         #pragma surface surf Lambert alpha
 
         struct Input {
             float3 viewDir;
             float2 uv_Maintex;
         };
         
         float4 _RimColor;
         float _RimPower;
         sampler2D _MainTex;
 
         void surf (Input IN, inout SurfaceOutput o) {
             o.Alpha = 0;
             
             half rim = 1.0 - saturate(dot(normalize(IN.viewDir), o.Normal));
             o.Emission = _RimColor.rgb * pow(rim, _RimPower);
         }
         ENDCG
     }

Thanks!